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Search.setIndex({docnames:["appendix/demos","appendix/demos-01","appendix/demos-02","appendix/demos-03","appendix/demos-04","appendix/demos-05","appendix/demos-06","appendix/linear-algebra","frontmatter","genindex","intro/algorithms","intro/conditioning","intro/demos/algorithms-horner","intro/demos/float-accuracy","intro/demos/float-arithmetic","intro/demos/float-julia","intro/demos/stability-quadbad","intro/demos/stability-quadgood","intro/demos/stability-roots","intro/floating-point","intro/next","intro/overview","intro/stability","ivp/adaptive","ivp/basics","ivp/demos/adapt-basic","ivp/demos/adapt-sing","ivp/demos/basics-cond","ivp/demos/basics-first","ivp/demos/basics-sing","ivp/demos/basics-usage","ivp/demos/euler-converge","ivp/demos/implicit-ab4","ivp/demos/implicit-stiff","ivp/demos/rk-converge","ivp/demos/systems-exp","ivp/demos/systems-predator","ivp/demos/zs-LIAF","ivp/euler","ivp/implicit","ivp/multistep","ivp/next","ivp/overview","ivp/rk","ivp/systems","ivp/zerostability","leastsq/demos/fitting-pirate","leastsq/demos/fitting-tempfit","leastsq/demos/fitting-tempinterp","leastsq/demos/house-qr","leastsq/demos/normaleqns-instab","leastsq/demos/qr-qrfact","leastsq/fitting","leastsq/house","leastsq/next","leastsq/normaleqns","leastsq/overview","leastsq/qr","linsys/condition-number","linsys/demos/condition-bound","linsys/demos/flops-loglog","linsys/demos/flops-lufact","linsys/demos/flops-mvmult","linsys/demos/interp-vander","linsys/demos/lu-factors","linsys/demos/lu-function","linsys/demos/lu-gauss","linsys/demos/matrices-julia","linsys/demos/norms-matrix","linsys/demos/norms-vector","linsys/demos/pivot-fail","linsys/demos/pivot-fixed","linsys/demos/structure-banded","linsys/demos/structure-cholesky","linsys/demos/structure-symm","linsys/demos/structure-timing","linsys/demos/systems-backslash","linsys/demos/systems-triangular","linsys/efficiency","linsys/linear-systems","linsys/lu","linsys/matrices","linsys/next","linsys/norms","linsys/overview","linsys/pivoting","linsys/polyinterp","linsys/structure","localapprox/B-splines","localapprox/adaptive","localapprox/demos/adapt-motive","localapprox/demos/adapt-usage","localapprox/demos/fd-weights","localapprox/demos/fdconverge-1","localapprox/demos/fdconverge-2","localapprox/demos/fdconverge-round","localapprox/demos/int-antideriv","localapprox/demos/int-extrap","localapprox/demos/int-trap","localapprox/demos/interp-cond","localapprox/demos/interp-global","localapprox/demos/interp-pwise","localapprox/demos/pwlin-converge","localapprox/demos/pwlin-hat","localapprox/demos/pwlin-usage","localapprox/demos/splines","localapprox/fd-converge","localapprox/finitediffs","localapprox/integration","localapprox/interpolation","localapprox/next","localapprox/overview","localapprox/pwlin","localapprox/splines","nonlineqn/demos/fp-converge","nonlineqn/demos/fp-spiral","nonlineqn/demos/newton-converge","nonlineqn/demos/newton-line","nonlineqn/demos/newton-usage","nonlineqn/demos/nlsq-MM","nonlineqn/demos/quasi-levenberg","nonlineqn/demos/roots-bessel","nonlineqn/demos/roots-cond","nonlineqn/demos/secant-converge","nonlineqn/demos/secant-iqi","nonlineqn/demos/secant-line","nonlineqn/demos/system-iter","nonlineqn/demos/system-usage","nonlineqn/fixed-point","nonlineqn/newton","nonlineqn/newtonsys","nonlineqn/next","nonlineqn/nlsq","nonlineqn/overview","nonlineqn/quasinewton","nonlineqn/rootproblem","nonlineqn/secant","refs"],envversion:{"sphinx.domains.c":1,"sphinx.domains.changeset":1,"sphinx.domains.citation":1,"sphinx.domains.cpp":1,"sphinx.domains.index":1,"sphinx.domains.javascript":1,"sphinx.domains.math":2,"sphinx.domains.python":1,"sphinx.domains.rst":1,"sphinx.domains.std":1,sphinx:56},filenames:["appendix/demos.md","appendix/demos-01.md","appendix/demos-02.md","appendix/demos-03.md","appendix/demos-04.md","appendix/demos-05.md","appendix/demos-06.md","appendix/linear-algebra.md","frontmatter.md","genindex.md","intro/algorithms.md","intro/conditioning.md","intro/demos/algorithms-horner.ipynb","intro/demos/float-accuracy.ipynb","intro/demos/float-arithmetic.ipynb","intro/demos/float-julia.ipynb","intro/demos/stability-quadbad.ipynb","intro/demos/stability-quadgood.ipynb","intro/demos/stability-roots.ipynb","intro/floating-point.md","intro/next.md","intro/overview.md","intro/stability.md","ivp/adaptive.md","ivp/basics.md","ivp/demos/adapt-basic.ipynb","ivp/demos/adapt-sing.ipynb","ivp/demos/basics-cond.ipynb","ivp/demos/basics-first.ipynb","ivp/demos/basics-sing.ipynb","ivp/demos/basics-usage.ipynb","ivp/demos/euler-converge.ipynb","ivp/demos/implicit-ab4.ipynb","ivp/demos/implicit-stiff.ipynb","ivp/demos/rk-converge.ipynb","ivp/demos/systems-exp.ipynb","ivp/demos/systems-predator.ipynb","ivp/demos/zs-LIAF.ipynb","ivp/euler.md","ivp/implicit.md","ivp/multistep.md","ivp/next.md","ivp/overview.md","ivp/rk.md","ivp/systems.md","ivp/zerostability.md","leastsq/demos/fitting-pirate.ipynb","leastsq/demos/fitting-tempfit.ipynb","leastsq/demos/fitting-tempinterp.ipynb","leasts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14,128,130,132,134],abrupt:25,abs:[13,16,17,18,34,37,46,68,89,91,94,95,98,114,115,116,123,124,129,130,136],abs_accuraci:13,absenc:88,absolut:[0,1,11,19,23,24,44,83,85,89,99,108,109,112,135],abstol:[31,32,34],academ:[80,137],academi:[24,110],acceler:[24,85],accept:[18,23,36,44,87,89,106,129,134,135],access:[10,15,20,51,67,71,80,112],accord:[7,10,52,107,135],accordingli:[39,90,111],account:[7,25,40,55,85,106],accumul:[19,21],accur:[13,16,17,19,21,22,23,31,32,33,34,39,45,50,80,87,89,90,96,97,98,106,107,108,112,115,121,129],accuraci:[0,1,6,11,16,22,23,24,25,34,38,39,40,42,43,44,45,59,77,80,85,89,91,94,95,98,107,108,111,113,120,128,134,137],accurate_digit:13,achiev:[21,40,52,106,108,128,133],acosh:22,across:[19,21,67,68,80,136],act:[22,30,84,86],action:112,actual:[15,18,19,23,24,25,27,33,50,52,63,78,83,85,86,87,88,91,106,119,129,130,135,136],adam:[39,45],adapt:[0,5,6,8,22,87,121],add:[10,11,12,38,39,58,63,66,78,85,87,89,97,108,112,113,132],added:[7,21,89,119],adding:[7,11,80,81,87],addison:137,addit:[10,11,14,19,22,43,44,57,67,78,80,83,85,87,113,129,134],addition:[7,129],address:[10,23,44,54,79],adequ:43,adjac:[15,84,88,112,113],adjoint:[67,74],adjust:[15,23,39],admonit:88,adopt:[40,129],advanc:[20,39,41,42,54,82,86,88,109,113],advantag:[7,19,87,107],advis:55,aesthet:107,affect:[23,83,84,87,88,128],affix:129,after:[10,12,44,63,77,80,83,85,87,107,113,128,132,134],again:[7,22,24,47,52,53,58,74,85,86,95,97,107,108,113,116,135],against:[53,123,129],ago:82,agre:[38,113,114],ah04:[110,137],ahead:45,aid:[19,110,132],air:24,alfio:137,algebra:[22,40,41,43,52,53,55,56,57,64,78,79,81,82,83,84,87,89,107,111,112,113,132,133,135,137],algorithm:[11,17,18,21,22,55,57,59,62,63,73,78,82,83,84,85,87,88,89,107,108,110,112,119,128,129,131,132,134,136,137],algortihm:128,align:[69,79,85,95],all:[7,10,11,12,13,15,16,18,19,22,24,38,42,43,44,45,48,52,56,57,58,60,62,63,65,67,78,80,81,82,83,84,85,86,87,88,89,94,96,99,106,107,109,111,112,113,120,122,128,130,132,134,136],alloc:[15,75,86],allow:[21,24,39,52,56,57,58,73,80,85,108,112,113,134],almost:[19,21,25,31,79,81,96,100,115],alon:[7,53,80,81,89,115],along:[36,53,115],alpha:[24,43,44,45,52,53,58,77,79,80,83,108,109,119,128,129,136],alpha_1:40,alpha_:40,alpha_n:19,alreadi:[18,55,79,80,108],also:[7,8,10,12,13,19,21,22,23,28,35,36,38,39,40,41,42,45,53,54,55,57,58,65,66,72,75,80,83,85,87,88,89,107,108,109,113,118,119,128,129,130,131,132,134,136],alter:19,altern:[0,1,22,38,57,84,85,87,88,113,129,132,134],although:[24,39,40,58,83,89,107,108,113,119,134],altogeth:113,alwai:[7,19,22,24,29,44,55,57,66,73,81,87,107,109,120,128,132,134,135,136],am1:40,am2:[33,39,40],am3:40,am4:[33,40],am5:40,amaz:132,ambigu:10,america:137,american:43,among:[44,110,112,131,135],amount:[11,26,34,43,54,85,119,122,128,132],amplifi:[45,55],amplitud:132,amvw15:[131,137],analog:[7,19,57,79,107,111,113,134],analysi:[7,23,40,44,45,53,78,82,83,106,107,109,130,134,137],analyt:[24,40,96,128,136],analyz:[84,136],anchor:85,andrew:137,angl:[44,53,83],ani:[7,10,11,12,19,22,23,24,30,38,39,45,49,52,53,55,57,58,59,67,72,77,78,79,80,83,85,87,88,95,98,104,107,108,109,112,113,122,128,129,130,133,134,135],annot:86,anomali:[47,48],anonym:[10,44],anoth:[7,10,11,22,28,39,44,49,53,57,58,73,77,80,81,83,85,87,89,98,108,109,112,113,126,128,131,134,135],ans:15,answer:[11,22,33,38,39,40,44,56,59,76,77,80,86,89,115,126,128,135],anticip:134,antideriv:[78,96,108],antidifferenti:108,anyth:[66,128],anywai:40,anywher:108,apart:10,appar:135,appeal:[108,112],appear:[7,11,14,23,26,36,40,44,53,55,58,85,87,88,94,107,108,112,113,117,135],append:[40,113,129,130,136],appl:34,appli:[8,10,11,16,18,22,23,24,37,38,39,43,44,45,49,52,53,57,63,67,68,74,78,80,83,84,89,93,95,97,107,108,112,113,115,116,127,128,129,131,132,134,135,136,137],applic:[19,22,24,43,44,48,52,53,54,83,87,107,108,110,113,128,131,133,134,136,137],approach:[11,26,36,44,45,79,89,96,106,108,109,113,128,132,137],appropri:[32,39,52,89,106],approx:[11,16,19,23,38,45,46,50,52,55,59,89,106,107,108,114,115,128,129,130,134,135,136],approxim:[11,13,19,22,23,32,34,38,40,43,45,46,52,58,78,84,85,89,93,98,106,107,108,110,111,113,114,115,117,121,125,127,128,129,132,133,134,135,136],april:137,arbitrari:[0,5,56,81,85,132],arbitrarili:[11,81,88,99],arctan:38,area:[10,24,96,108],aren:19,argmin:52,argument:[10,28,38,43,44,58,112,129,130,134],arieh:137,aris:[39,87,89,107,133],arithmet:[0,1,10,11,20,21,22,58,78,79,80,84,85,87,106,135],armi:108,around:[10,24,40,80,84,106,111,121,126],arrai:[7,12,15,18,23,30,33,35,43,46,47,48,49,51,59,63,64,65,66,67,68,70,71,72,73,74,75,76,77,80,81,84,92,93,97,103,114,116,119,120,123,124,126,127,130],arrang:88,arriv:[45,52,57,74,80,134],arrow:[10,115],articl:[20,41,82],artifici:[10,50,119],ascend:[10,12,63],ashlei:7,asid:80,ask:[11,22,23,58,88,112,124,132,134],aspect:[8,10,78,80,81,88],aspect_ratio:[68,115,122,130],assembl:[88,113],assert:[78,128],assess:109,assign:118,associ:[7,10,14,63,80,88,108,135,137],assum:[10,11,19,23,24,31,34,38,42,44,58,62,78,83,86,88,89,107,108,112,128,129,134,135,136],assumpt:[23,129,134,136],asymptot:[46,53,55,84,87,93,108,129,133],ata:55,atk89:[41,137],atkinson:[41,110,137],atol:[90,91,97,98],attach:85,attempt:[23,37,45,80,88,134],attend:79,attent:[19,85,134],attract:[24,57],au_1:44,augment:[66,80],august:137,aurentz:137,australia:137,author:131,automat:[49,55,87,89],avail:[8,18,24,44,45,56,80,85,106,107,108,129,131,132],averag:[19,25,47,48],avoid:[11,12,22,23,62,66,79,80,87,113,134,136],awai:[21,115,128,131],award:[110,131],axes:[36,44,52],axi:[34,39,53,58,78,108,122,136],b_0:106,b_0f:40,b_1:[7,43,78,79,106],b_1k_1:43,b_1n:78,b_2:[7,43,79,106],b_3:[79,106],b_4:[79,108],b_6:108,b_bound:59,b_i:[19,106],b_j:[40,43],b_k:113,b_kf:40,b_kf_:40,b_n:[7,79],b_s:43,b_u:87,b_ub_:87,back:[21,23,56,63,74,88,111],backend:[31,32,34,37,62,90,91,93,94,95,97,98,102,105,121],backslash:[0,2,50,52,55,57,58,63,71,79,84,87,130,132],backsub:[55,57,65,66,70,71,77,78,79],backup:134,backward:[18,21,57,66,78,79,80,84,85,107,108,120,129,131,134,135,137],backward_err:120,bad:[16,63],badli:[58,59,129],baer:[44,137],bailei:137,balanc:85,banana:132,band:[0,2],bandwidth:[72,84,87,88],bar:7,barbara:7,barrier:45,base:[10,19,23,40,58,80,87,89,106,107,112,117,130,132,135],baselin:132,bashforth:[39,40],basi:[34,39,80,88,108,111,112,113,136],basic:[23,38,39,81,88,96,130],bau:[82,137],bcp96:[41,137],bd1:40,bd2:[39,40,45],bd3:[40,45],bd4:40,be86:[44,137],beauti:45,beautifulli:115,becaus:[10,11,15,19,23,26,28,38,39,40,43,44,45,50,51,55,56,58,59,76,78,79,80,83,84,85,87,88,106,107,108,109,112,119,128,130],becom:[11,16,23,31,40,44,54,57,58,78,80,87,88,106,107,112,113,115,129,130,132,134,136],been:[8,24,29,54,83,85,131],befor:[11,19,21,39,44,59,64,68,74,76,79,81,85,107,108,112,113,117,122,123,125,127,132,136],befriend:87,begin:[7,10,11,19,22,23,24,38,39,40,43,44,45,52,53,55,57,58,69,74,78,79,80,81,82,83,85,86,87,88,106,107,108,112,113,128,129,130,132,134,135,136],beglei:137,behav:[22,27,67,108],behavior:[23,24,38,55,128,129],behind:[40,136],being:[8,10,45,80,82,106,107,108,112,113,128,129,134,135],believ:[89,109],bell:19,belong:[7,19,81,88,113],below:[19,22,38,44,49,52,57,72,80,81,84,85,89,108,129,130,135,136],benefit:[23,87,108,132],bengt:137,berk:137,bernoulli:108,bernstein:88,besid:113,bessel:[0,4,135],besselj:121,best:[22,23,47,52,56,58,65,87,97,131,132,136],beta:[43,44,53,55,58,77,79,80,108,109,119,128],beta_n:19,better:[11,19,23,52,88,89,107,108,113,119,131,132,134,135],between:[11,12,14,15,19,22,23,39,40,42,45,67,80,83,84,85,86,88,99,101,106,108,111,112,113,122,125,128,129,132,133,134,135,136],beyond:[11,57,63,108,128],bezier:88,bf00609587:137,bf01:[110,137],bifurc:137,big:[78,84,99],biggest:136,bigl:[7,10,11,22,23,24,38,39,40,43,44,53,55,58,69,78,80,81,87,89,106,107,108,109,112,113,117,125,128,130,132,134,135,136],bigr:[7,10,11,22,23,24,38,39,40,43,44,53,55,58,69,78,80,81,87,89,106,107,108,109,112,113,117,125,128,130,132,134,135,136],billion:10,binari:[15,19,110,134],biologi:137,birth:[24,109],bisect:89,bit:[11,15,19,21,30,36,39,40,91,106],bitstr:15,bjl05:[89,108,137],bjorck96:[54,137],black:[27,91,95,125],blend:[23,136],blew:82,blink:[132,137],block:[53,67,80,88,134],blood:24,blow:[26,89],blowup:[26,29],blug7:[],bm98:[132,137],bmatrix:[7,39,52,53,55,57,58,79,80,81,83,85,86,87,88,113,130,132,134],bogacki:23,boil:111,bold:[7,81],boldfac:[7,39,44,81],boldsymbol:[7,39,52,53,55,81,83,113,130,132,134],book:[7,8,10,12,21,22,44,56,57,81,128],bool:[64,71],boor:[110,137],boost:[24,40,43],born:109,borr:[54,137],borrow:88,boston:137,both:[7,11,14,22,23,24,27,36,39,40,41,42,43,44,51,52,56,72,80,83,87,88,89,90,94,106,107,109,112,113,116,128,134,136],bother:[21,40],bottom:[66,88,109],bottomleft:[32,34,94],bottomright:[33,47,48,95,115,119,124],bounc:42,bound:[0,2,11,19,23,24,27,38,43,45,58,78,85,89,106,108,109,112,128],bowden:82,bracket:[10,43,67],bradbrook:137,braun:[8,137],breakdown:[14,85],brenan:[41,137],brent:136,breviti:10,brew:24,bri03:[44,137],brief:[54,126],briefer:79,bring:136,britton:137,broadcast:67,broadli:42,broke:[71,87],broken:108,brook:137,brosch:[132,137],broughton:137,broyden:132,bs23:23,bspline1:88,bspline:88,bsplinegraph:88,bsplinehand:88,bsplineinterp:88,bu_1:44,bud:131,bug:29,build:[10,48,53,67,78],built:[41,59,61,62,85,87],bulk:136,bump:123,burden:[110,137],bureau:86,busi:137,bwb:[132,137],c3po:133,c_0:112,c_1:[10,43,45,52,55,78,86,88,108,132],c_1h:43,c_1n:78,c_2:[10,43,45,52,55,78,86,88,108,132],c_2h:43,c_2t:52,c_2z:52,c_3:[10,52,55,86,108,132],c_3t:86,c_3z:52,c_4:108,c_4z:52,c_7:52,c_i:[43,86],c_j:45,c_k:[45,88,108,112,113],c_m:132,c_n:[10,52,86,112,132],c_nt_1:86,c_nt_2:86,c_nt_3:86,c_nt_n:86,caffein:[23,24,137],calcul:[10,11,13,16,19,21,22,38,42,43,44,57,80,106,107,112,114,116,119,130,134,136],calculu:[22,38,52,78,81,96,108,111,112,128,129,134,136],call:[7,10,11,12,15,19,21,22,23,24,38,39,40,41,42,43,44,45,51,53,54,55,56,57,71,72,79,80,83,84,85,87,88,89,106,108,109,112,113,117,118,125,128,129,130,132,134,135,136],callabl:[30,104],caller:[10,134],cambridg:137,came:108,camp:42,campbel:137,can:[7,8,10,11,12,13,15,16,18,19,20,21,22,23,24,28,29,30,31,35,36,38,39,40,41,43,44,45,46,48,49,51,52,53,54,55,57,58,60,63,65,66,67,68,71,72,74,75,78,79,80,81,83,84,85,86,87,88,89,91,92,94,96,97,99,106,107,108,109,110,111,112,113,114,115,116,117,118,119,121,122,123,125,127,128,129,130,131,132,133,134,135,136],cancel:[11,16,19,21,22,53,57,77,85,89,106,108,111,113],candid:[88,107,109,112,132],cannot:[11,19,24,38,45,51,56,58,78,85,87,89,106,108,113,132,135,136],cap:24,capabl:85,capit:[7,81],capita:24,caption:88,cardin:[0,5,108,109,111,113],cardinalexpress:112,care:[23,38,89,128],career:131,carefulli:[39,51,89],carl:[110,137],carolyn:137,carri:[44,74,80,86,87,136],catastroph:33,cauchi:128,caus:[22,38,45,53,58,67,76,80,85,87],cccc:[23,43],ccccc:43,cdate:52,cdot2:[38,39],cdot5:52,cdot:[7,10,11,19,22,38,43,45,46,52,53,55,57,78,79,80,83,85,86,88,106,108,112,113,119,128,129,130,132,135],celebr:45,cengag:137,censu:[52,57,63,86,130,132],center:[88,106],central:[72,79],centuri:[121,130,132],certain:[24,52,53,56,58,84,85,86,87,88,128,137],certainli:[58,88],cf13:[41,137],chain:[11,16,43],challeng:[129,131],chang:[7,11,19,21,22,23,24,25,31,36,39,40,42,44,53,55,58,59,70,80,84,87,88,107,108,109,115,118,129,133,134,135,136],chapter06:26,chapter:[8,21,24,30,39,44,52,54,56,63,79,80,83,86,87,89,109,111,131,133,134,135],charact:[7,81,84,137],character:[22,40,56,107,137],characterist:[10,43,88,112],charl:137,cheap:134,check:[11,23,24,45,68,76,79,87,89,98,114,120,123,126,127],chenei:[110,137],china:[0,2,79,86,112],choic:[10,15,19,22,28,45,52,56,58,79,82,85,87,112,128,132,136],choleski:[0,2,55,57,84,87],choos:[19,52,53,107,109,112,124,136],chose:22,chosen:[19,23,73,81,83,85,87,91,99,108,115,134],christian:137,circl:[44,68,83],circular:121,circumst:[22,23,53,67,129,130],cite:131,ck12:[110,137],clamp:121,clarif:58,clarifi:38,clariti:[10,81,113,119],clash:12,classic:[10,19,82,129,131,137],classifi:132,clean:112,cleaner:88,clear:[10,15,25,37,38,44,58,77,78,79,93,111,112,114,117,119,125,128,129],clearer:[40,94],clearli:[23,89,99,108,119],clever:131,clinic:137,clone:80,close:[11,18,19,22,24,26,30,36,42,47,56,76,85,88,91,106,112,113,114,119,124,126,128,131,132,134,135],closer:[11,23,27,106,107,115,117,134],closest:[19,55,107,129,130,134],clue:[37,79],cluster:137,coarsest:97,code:[19,23,32,39,43,44,46,53,78,80,81,85,86,87,88,97,106,109,112,120,129,130,134],coeff:[18,107,114],coeffici:[10,11,12,18,35,39,42,45,46,52,63,86,88,106,107,109,112,113,132],cofactor:80,coffe:24,coh94:[20,137],cohen:[20,137],coin:19,coincid:[52,56,88],coincidentknot:88,cole:137,collect:[7,10,38,57,81,88,106,113],collis:[130,134],colon:67,color:[91,95,125],column:[7,36,39,49,52,53,55,56,57,58,64,66,67,68,74,79,80,83,85,87,88,91,97,109,113,126,130,134],com:12,combin:[7,11,23,39,40,53,80,81,88,97,106,107,108,109,111,112,131,134],come:[10,11,12,23,28,40,43,44,57,80,85,88,89,91,134,136],comma:[10,67],command:[10,12,53,55,57,69,72,76,77,79,80,81,87,107],comment:[12,67],common:[11,15,23,36,52,57,80,87,107,131,134],commonli:[19,40,43,44],commun:88,commut:7,compact:[10,46,86,107],compani:137,companion:131,compar:[10,11,19,31,34,38,39,46,48,52,53,61,65,77,78,80,85,89,106,107,108,113,116,130,132,136],comparison:[0,5,60,85,106,131,136,137],compat:[67,81,83,85],compel:132,competit:[24,39],compil:[12,60,61],complement:[10,128],complementari:[40,56],complet:[10,21,24,38,39,40,43,44,59,80,85,88,89,108,112,119,128,131],complex:[7,11,43,45,67,81,83,84,131,134],complic:[11,22,39,42,44,60,83,107,111,113,132,134],compon:[7,10,36,44,58,79,119,120],componentwis:[7,83,87,130],composit:[11,108],comprehens:[79,84,86,110],compress:57,compris:113,comput:[8,10,11,16,17,18,19,22,23,24,27,30,34,35,36,38,39,40,43,44,46,52,55,56,57,58,59,62,76,79,80,82,83,84,85,86,87,88,89,97,100,106,107,108,109,110,111,112,113,114,115,117,126,127,128,129,130,131,132,133,134,135,136,137],computation:[55,57,71,80,108],concaten:[7,67,88],conceiv:[108,134],concentr:[24,119,137],conceptu:134,concern:[24,39],concis:[40,45,55,112],conclud:[11,19,78,87,88,112,128,136],conclus:[11,22,38,40,61,78,80,106,128,135],cond:[50,55,59],condit:[0,2,4,5,6,16,18,21,22,23,36,38,42,44,48,50,52,53,57,79,84,85,87,88,99,101,106,107,128,129,131,132],confirm:[22,108],confus:[19,45,79],confusingli:57,conjectur:46,conjug:[7,67,81,84],conn:[131,137],connect:[7,23,38,40,80,81,108,112,131],consecut:[88,101],consequ:[19,85,87,88,89,107,112,135],consequenti:19,conserv:23,consid:[7,11,18,19,24,27,31,32,34,37,38,39,42,43,44,45,52,56,57,58,78,79,80,81,85,87,88,89,91,97,100,106,107,108,109,112,113,122,128,129,132,134,135],consider:[7,78,115],consist:[19,21,38,45,81,98,109,128],constant:[11,15,19,21,23,24,35,38,39,40,42,43,44,45,52,58,78,88,106,107,108,112,113,114,123,128,129,130,132,133,135,136],constrain:107,constraint:[56,132,133],construct:[18,23,31,32,34,57,63,75,84,85,86,101,109,111,112,113,114,125,128,129,130,134,136],contain:[38,83,88,112,119,128,131,136,137],content:[80,84],context:[7,11,24,63,73,80,81,85,88,109,112,133,136],continu:[11,19,22,42,47,52,53,54,63,81,83,86,88,95,107,109,110,111,112,113,116,126,128,129,132,134,135,136],contour:132,contract:88,contradict:39,contradictori:128,contrari:57,contrast:[19,40,122],contribut:[23,106,137],control:[23,88,129,134],conveni:[7,11,12,19,36,42,52,57,63,67,80,88,107,108,109,119,130,134],convent:[7,40,78,81,94],converg:[0,3,4,5,6,23,24,27,33,39,43,45,52,83,89,91,94,105,107,108,115,120,126,127,130,131,133,134,135],convers:[7,15,22,45,81,84,88,89,135,137],convert:[15,36,44,51,80,84,87,88,111,115,130,131],convinc:88,cook:119,cool:7,coordin:[10,115,121],cope:88,copi:[53,80,84,129],copyright:8,core:[12,76,82,111],corless:[41,137],corner:80,cornerston:[129,133],corpor:131,correct:[10,14,16,18,38,44,49,58,79,85,86,106,112,115,128],correctli:[29,44,108],correspond:[23,24,55,67,74,83,112,119,134],cos:[11,22,24,39,43,44,50,52,53,55,67,68,78,80,89,90,91,92,93,94,106,108,112,113,119,121,124,130,132,134,135],cosh:22,cost:[23,39,80,89,97],cot:11,cote:[108,111],could:[10,11,23,31,38,39,42,44,45,52,53,61,62,74,76,79,80,85,88,100,107,108,113,114,116,126,128,132,134],count:[0,2,52,53,55,136],counter:134,counterclockwis:10,counterexampl:[7,81],counterpart:11,countless:121,countri:86,cours:[11,79,80,82,83,96,132,136,137],cover:[8,41,82,87,112,133],cpc:18,crazi:48,creat:[7,10,19,22,24,53,63,66,67,80,84,85,87,88,104,109,112,113,118,130,132],criterion:[47,52,89,129],critic:[44,81],cross:136,crossov:95,crucial:[10,19,107,108,113],crude:24,cryptic:86,csv09:[131,137],ctor:137,cubic:[0,5,47,52,63,86,88,99,101,108,109,110,111],cubicsplineinterpol:[101,109,111],culmin:85,cumsum:46,cumul:46,curiou:[85,89,132],current:[63,132,134,136,137],curriculum:137,curv:[19,23,36,38,44,46,48,63,86,88,91,108,116,117,119,130,134,137],custom:53,customari:[58,78],cut:[93,98,106],d2a8:[],d_1:[52,113],d_2:[52,113],d_3:52,d_4:52,d_5:52,d_k:113,d_n:113,dai:52,darlen:137,dartt:137,dash:[31,32,34,46,60,61,68,91,94,95,98,102,105,117,119,124,125],data:[0,3,10,11,18,21,22,24,28,39,45,54,55,56,58,59,60,61,63,76,80,84,86,88,89,99,100,101,104,108,109,111,112,113,119,130,131,135,137],datafram:[],dataset:22,date:[41,63,134],davi:[110,137],david:137,ddot:[7,43,57,58,87,113],deal:[24,43,54,57,78,81,89,129,133],dealt:11,death:[24,132],deboor78:[110,137],decad:48,decai:132,decemb:137,decent:89,decid:[11,23],decim:[11,17,19,21],decis:[89,129],declar:10,decreas:[43,91,94,95,98,106,114,128,133,134],deduc:[36,85],deeper:112,defect:80,defici:57,defin:[7,10,11,12,19,22,24,28,31,35,38,39,40,42,44,45,49,52,53,55,56,57,58,66,67,79,80,81,83,84,85,87,88,89,91,103,106,107,108,109,111,112,113,115,120,126,127,128,129,130,132,133,134,135,136],definit:[7,10,11,21,28,38,40,41,43,44,49,52,57,58,63,73,80,81,83,84,86,88,106,107,108,109,111,112,113,118,128,129,134,135],deflat:135,deg:40,degener:135,degre:[10,11,12,40,47,48,52,55,56,57,58,86,88,109,135],delawar:131,delet:[38,57,108,113],delft:137,delta:[24,58,89,106,109,134,135],delta_a:89,delta_r:89,demo:88,demonstr:[24,39,55,57,79,80,81,85,87,88,89,136],denom:107,denomin:[11,53,80,129,134],denorm:19,denot:[7,10,21,38,58,81,88,109,113],dens:[75,87],depend:[7,11,12,19,22,24,35,36,38,39,42,43,44,50,52,55,58,79,80,81,85,106,107,108,112,132,133],deriv:[8,11,23,24,31,38,39,42,43,44,52,57,58,79,83,88,92,106,108,109,110,111,112,113,116,117,119,125,128,129,130,133,134,135,136,137],descend:79,descent:134,describ:[7,11,23,38,42,44,45,53,54,76,79,81,84,88,112,130,132,134],descript:[10,19,39,44,113],design:[49,83,109,110,111,131],desir:[10,43,81,88,89,107,113,128],despit:[14,89],destabil:55,destroi:[49,85],det:80,detail:[11,19,22,23,39,40,43,53,54,85,87,106,108,109,110,113,131,134,136],detect:[22,23,24,52,73,76,89,112],determin:[15,24,43,45,52,80,85,86,87,88,108,109,113,116,128,129,130,132,134,135,136],develop:[108,131],devis:53,dfdx:[92,116,117,118,129],dfrac:[11,58,112,129],diag:72,diag_main:72,diag_minuson:72,diag_pluson:72,diagm:[67,72,74,75,77,88,113],diagon:[7,49,53,57,58,64,67,72,74,79,80,83,84,85,87,113],did:[19,49,80,131,134,135],dif:[102,105],diff:[25,88,113],diffeqbas:29,differ:[0,5,10,11,14,15,19,21,22,23,27,30,31,38,39,40,42,44,45,52,55,65,71,77,80,83,84,86,88,89,92,94,99,100,102,105,108,110,111,112,113,119,128,129,130,132,133,135,136],differenti:[11,24,35,38,39,41,42,52,107,111,112,129,134,135,137],differentialequ:[24,28,31,32,34,42,44],differntialequ:30,difficult:[21,78,87,96,108,111,128,130,134],difficulti:[10,20,135],digit:[11,13,16,19,21,22,24,50,58,59,77,80,89,97,106,115,129,131,132],dim:68,dimens:[7,44,53,67,68,81,83,84,88,126,130,134],dimension:[7,53,81,83,130,134],dimensionless:19,direct:[22,83,88,134],directli:[7,11,15,22,43,53,55,57,67,83,87,88,113,129],disappear:[122,130],discontinu:[88,113],discov:128,discrep:132,discret:[21,30,36,38,39,42,43,106,111],discuss:[20,21,24,40,53,54,79,80,83,84,89,129,130,131],diseas:44,disp:52,displac:[85,121,122],displai:[13,33,115],displaystyl:[7,24,46,58,79,80,81,83,89,97,108],distanc:[19,21,24,52,63,83,88,122,128,132,135],distinct:[40,45,109,113,116],distinguish:[38,108],distribut:[7,19,39,89,112],disturb:19,diverg:[24,27,128,129,134],divid:[38,40,58,87,93,130,132],divis:[22,38,67,78,85,114,129,135],do_integr:89,doc:88,document:[7,10,26],doe:[11,12,19,23,24,38,39,45,48,52,53,55,57,58,59,78,79,80,81,83,85,87,89,107,108,128,134,135],doesn:[15,23,46],doi:137,doing:[40,53,62,87,108,114],domain:[11,23,38,42],domin:[62,78,87,95,97,106],don:[18,23,28,31,36,38,53,58,59,80,84,85,87,112,114,116,123,126,130,134,135,136],donald:[131,137],done:[10,12,19,23,24,29,53,67,79,80,81,83,86,87,89,108,126,134,136],doom:45,dose:24,dot:[22,24,63,67,71,78,83,92,95,109,112,113,130],doubl:[11,14,15,18,21,23,59,80,88,89,97,98,112,116,126,127,129,135,136],doubli:55,doubt:136,dougla:137,down:[19,58,68,74,77,95,97,106,111,113],download:12,downward:[87,112],dozen:82,dr14:[110,137],dramat:[11,22,75],drastic:135,draw:[19,83,88,125,134],drawback:[10,39,89,136],drawn:122,drink:24,drip:24,driscol:[8,26,29,137],drown:45,drum:121,drumhead:121,dry:137,dtmin:29,dudt:37,due:[11,22,24,27,85,108,136],dummi:107,dump:12,duplic:89,dupont:131,dure:[19,80,82,84,85,107,131,132,134],dwarf:78,dydx:129,dynam:137,e48b7b93:[],e_0:38,e_i:[23,38],e_k:52,each:[7,10,11,12,16,18,19,21,22,23,24,27,31,34,36,38,39,40,42,43,44,45,52,53,58,62,67,78,79,80,81,83,85,87,88,89,94,97,98,101,106,107,108,109,112,113,114,117,118,128,129,132,133,134,135,136],earlier:[22,40,55,58,80,130,134,135],earth:52,eas:28,easi:[19,24,45,77,79,81,83,94,108,109,116,123,128,129,134],easier:[11,24,89,128,129,136],easiest:[11,88,114,128],easili:[11,16,21,24,40,44,52,56,57,79,85,112,114,130,132,134,135,136],ecolog:44,edg:[52,112,122],edit:137,editor:137,educ:[136,137],effect:[12,21,22,24,38,53,85,99,106,109,122,130,135,137],effici:[10,23,34,40,53,57,71,73,80,84,88,95,106,107,112,136],effort:10,eigenvalu:[87,131],eight:88,eighth:108,either:[29,38,44,57,84,85,89,109,112,128,129,136],elaps:[60,61,62,87],elect:110,electron:112,eleg:[10,107,108],element:[7,12,15,18,19,30,33,46,47,48,49,53,59,62,63,65,66,67,70,71,72,76,77,79,80,81,83,84,85,87,92,93,97,103,112,114,116,119,120,123,124,126,127],elementari:[7,11,16,19,22,53,55,66,80,85,107,112,137],elementwis:[7,63,67,114],elimin:[0,2,53,74,78,84,85,87,113],ell:87,ellips:68,ellipsoid:[130,134],ellipt:[130,134],els:[78,87,89,107,112,132,134],elseif:[107,112],elsevi:137,elsewher:[129,131],emb:129,embed:[108,126],emph:[7,88],emphas:[7,10,81,82,85],emphasi:110,emphat:39,empir:[21,56,111],emploi:[23,40,43,55],empti:79,encapsul:53,enclos:[10,67,83],encod:36,encount:[10,11,45,83,84,134],end:[7,10,11,19,22,23,24,25,31,32,33,34,35,36,37,38,39,40,42,43,44,45,49,52,53,55,57,58,59,60,61,62,66,67,69,78,79,80,81,82,83,84,85,86,87,88,89,90,91,94,95,98,102,105,106,107,108,112,114,115,116,118,119,120,121,123,124,126,127,128,129,130,131,132,134,136],endem:44,endpoint:[19,67,88,90,113,125,136],energi:56,enforc:78,engin:[59,77,137],enorm:[21,78],enough:[10,19,57,78,86,88,89,106,108,128,129,132,134,135],ensur:[66,84,99,113],enter:[10,16,19,67,109],entir:[16,23,38,40,42,67,113,122,130],entitl:131,entri:[7,10,35,40,58,64,66,67,71,75,76,79,80,83,84,85,86,87,88,113,119],enumer:[31,32,34,37,60,61,62,90],environ:10,enzym:119,epidem:[132,137],epidemiolog:44,eps:[14,15,50,53,58,59,95,129,130,134,136],epsilon:[11,15,18,19,21,23,38,44,50,59,65,85,89,129,134,135,136],epsilon_1:128,epsilon_2:128,epsilon_:[14,15,22,38,58,106,128,129,134,136],epsilon_k:[46,128,129,136],epsilon_kf:129,equal:[7,15,19,23,24,38,42,45,55,57,58,60,72,76,78,79,80,81,83,84,85,87,88,89,92,95,106,107,108,109,112,113,128,132,135,136],equat:[3,7,19,23,24,28,29,30,35,36,38,39,40,41,42,45,52,56,57,58,70,79,80,82,84,85,86,88,106,108,109,110,113,121,125,127,128,129,130,131,132,134,135,136,137],equilater:10,equilibrium:85,equispac:[107,112,113],equiv:[24,88],equival:[7,19,22,38,40,45,52,55,56,57,58,60,66,68,76,80,81,83,84,87,89,107,108,129,130,132,133,134,135,136],era:54,erf:89,erneux:[44,137],ernst:137,err:[23,31,32,37,77,90,91,93,95,98,102,105,114,116,123,124],err_2nd:97,err_4th:97,err_6th:97,err_ie2:34,err_rk4:34,errest:[91,96,97,98],error:[0,2,11,15,16,17,18,19,20,21,24,29,31,32,34,37,39,42,43,44,45,46,50,67,73,76,77,80,85,90,91,93,94,95,97,98,102,105,106,107,108,111,112,113,114,116,120,123,124,126,127,128,129,134,136,137],error_fd1:94,error_fd2:94,escap:129,especi:[19,39,79,126,134],essenti:[11,16,18,52,57,70,79,85,109,128,137],establish:[57,66,128],estim:[22,39,43,56,58,63,86,88,91,92,95,96,97,106,107,108,109,112,113,114,115,121,126,127,129,130,132,133,134,135,136,137],etc:[40,43,80,87,112],euclidean:83,euler:[0,6,39,40,42,43,44,89,108],european:137,evalaut:115,evalu:[10,12,22,23,24,30,34,39,40,42,43,52,63,78,86,88,89,91,96,97,104,106,107,108,110,112,113,124,125,128,134,135,136],even:[7,10,11,12,15,18,19,21,22,23,25,26,28,36,40,43,45,51,53,57,58,59,80,85,87,91,106,108,112,129,130,134,135],evenli:[19,67,113,136],eventu:[80,95,129,134],ever:[39,54,106,128],everi:[7,11,12,19,21,44,45,52,57,58,63,68,80,84,85,86,89,97,108,109,112,113,126,132,133],everydai:19,everyth:[0,6,11,29,39,42,77,78,108,134],everywher:[88,111,113],evid:[24,128],evolut:131,exa:88,exabezi:88,exact:[11,16,18,19,22,23,31,32,34,38,39,40,43,44,45,50,58,59,65,77,78,85,89,91,95,96,98,107,111,116,123,126,129,130,132,134,135,136],exact_valu:[92,93,94],exactli:[10,11,14,19,38,48,58,60,76,78,80,88,89,100,106,107,108,119,122,128,130,134,135,136],examin:88,exampl:[10,15,18,19,22,23,24,39,40,43,44,45,52,53,55,57,58,59,64,65,71,77,78,79,81,85,86,87,88,92,96,107,108,109,113,119,123,128,129,136],exce:[22,59],exceed:129,excel:110,except:[15,18,19,22,76,87],exchang:129,exclus:[24,52],execut:[10,12,88],exercis:[8,84,88],exhibit:21,exist:[7,19,28,29,81,84,87,108,112,128,129,130],exp:[10,22,24,25,27,35,37,46,52,67,93,94,95,96,97,98,102,104,105,113,114,116,117,118,119,120,123,125,126,127,132],expand:[67,106],expans:[17,40,43,80,108,111,112,128,129,135,136],expect:[11,15,16,19,23,31,38,45,58,65,67,78,89,97,102,105,106,108,109,127,132,134,135],expens:[71,80,108,134],experi:[10,17,52,60,62,82,86,87,128],experiment:[24,38,55,61,131,137],expert:23,explain:[16,21,22,23,38,39,40,80,81,83,85,86,87,107,113,128,134],explicit:[33,36,38,39,40,43,44,45,55,88,132],explicitli:[10,11,19,38,53,76,108,112,135],explod:37,exploit:[55,66,75,89,112],explor:[44,87,109,110],expon:[15,19,38,40,42,112,116,127,136],exponenti:[0,6,24,27,37,38,39,44,45,52,114,132],express:[7,11,19,22,38,40,43,48,52,55,57,59,64,67,78,79,80,85,106,107,108,112,113,121,128,132,134],extend:[7,40,81,130,133,135],extens:[10,56,106,130],extent:134,extra:[12,25,38,39,97,134],extract:[30,72,73,80,81],extran:88,extrapol:[0,5,63,89,111],extrem:[11,21,73,134],eye:132,eyelid:132,ezier:88,f743ccd5256c:[],f_1:[44,52,130,134],f_2:[44,52,130,134],f_3:130,f_i:[40,119,130],f_j:45,f_k:134,f_n:[52,130,134],f_t:43,f_u:43,face:111,fact:[7,11,15,24,26,38,39,53,55,58,59,71,79,85,88,106,107,108,111,112,113,122,129,130,135],factor:[0,2,3,11,23,24,25,38,39,49,55,56,62,71,75,78,84,85,87,88,93,94,97,98,106,107,113,114,128,131,133,135],fail:[24,39,70,79,80,87,89,134],failur:[0,2,26,80,85],fair:[19,110,137],fairli:[109,129,134],fall:42,fallen:24,fals:[60,78,88,130,134],famili:59,familiar:[7,52,81,108,112],famou:[46,132],famous:59,fanci:46,far:[18,23,39,56,80,83,96,113,129,134],fare:38,farther:[128,134],farthest:[130,134],fascin:46,fashion:23,fast:[10,39,131,134,136,137],faster:[71,84,87,116,128,131,133,136],fastest:[10,128],fausto:137,favor:23,favorit:111,fd1:[93,94,95],fd2:[94,95],fd4:95,fd_valu:92,fdjac:134,fdweight:[92,107],featur:[23,52,85,134],feel:[81,111],few:[10,12,23,40,44,58,98,105,115,124,126],fewer:[16,25,39,87],fibonacci:[45,136],fictiti:[88,112],field:[8,56],fig:[22,53,55,57,88,108],figur:[57,60,63,86,88,99,109,130,132],file:[8,10,126,129],fill:[38,39,43,49,96,132],fillion:137,fillon:41,film:137,filter:54,final_misfit_linear:119,final_misfit_norm:119,find:[7,10,11,16,17,18,19,20,22,23,24,36,38,39,40,43,44,45,46,50,52,53,55,57,58,70,78,79,80,81,82,83,84,85,86,88,89,96,98,107,108,109,110,112,113,114,115,116,117,119,120,121,122,125,126,128,129,130,131,132,133,134,135,136],findfirst:[88,113],finer:108,finish:[10,66,112],finit:[0,5,11,19,21,22,24,26,29,31,38,40,83,84,89,92,94,108,110,111,112,128,132,135],fire:44,first:[7,8,10,11,12,15,16,17,18,19,21,22,23,28,31,33,38,40,43,44,45,46,48,49,52,53,55,57,63,64,66,67,68,74,76,77,78,79,80,81,83,84,85,87,88,94,95,96,97,104,106,107,109,113,120,121,122,128,129,131,132,133,134,135,136,137],fit:[0,3,4,46,48,54,55,57,99,100,109,111,114,124,130,131,136,137],fitzhugh:[23,43,44],five:[11,81,88,89,92,107,113],fix:[0,4,11,19,23,28,37,38,39,85,89,109,131,133,134,135],flip:80,float64:[15,18,30,33,37,46,47,48,49,51,59,63,64,65,66,67,70,71,72,73,74,75,76,77,92,93,95,97,102,103,105,114,116,119,120,123,124,126,127],floatmax:[15,19],floatmin:15,flop:[0,2,53,55,61,84,85,87],flux:82,fly:[42,109],fnc:[12,25,26,31,32,33,34,65,66,70,71,72,77,90,91,92,98,99,102,103,104,105,118,119,120,123,127],fncbook:12,fnew:134,focu:[24,135],foil:129,follow:[7,10,11,12,14,18,19,24,33,38,39,40,44,45,50,52,53,54,55,57,58,64,66,71,78,79,80,81,83,85,87,88,107,108,109,111,112,113,115,119,126,129,130,132,134,135,136],foolproof:136,foot:38,footnot:[89,128],for98:[110,137],forc:[15,24,60,61,85,99,111],forev:[116,129],form:[10,19,23,24,38,39,40,43,44,51,52,53,57,80,83,84,86,87,88,107,108,109,111,113,116,119,128,129,130,132,134,136],formal:[10,11,19,22,35,38,109,128,129,135],format:[53,60],former:19,formul:[29,44,50,58,132,135],formula:[0,1,10,11,22,24,28,38,39,42,43,44,45,46,53,68,78,79,83,85,87,88,89,92,93,94,95,97,103,106,109,111,112,128,129,134,136],fornberg:[107,110,137],fornula:22,fortran:[83,131],fortun:[11,23,44,80,85,107,108],forward:[18,38,40,42,45,78,79,80,84,85,93,106,108,124],forwardsub:[55,65,70,71,77,78,79],found:[7,14,20,21,22,24,26,28,40,41,52,54,80,81,85,86,89,107,110,113,131,132,133,134,136],foundat:134,four:[23,39,44,49,63,77,81,85,88,106,112,113,130,134],fourth:[34,39,43,70,89,91,95,107,108,113],frac:[10,11,19,22,23,24,35,38,39,40,43,44,45,46,52,53,58,78,79,83,85,87,88,89,106,107,108,109,112,119,128,129,130,134,135,1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8,93,94,95,106,107,108,109,112,113,128,130,131,132,134,135,136],hps13:[54,137],hskip:87,html:[31,32,34,37,62,90,91,93,94,95,97,98,102,105,121],http:12,huge:[22,23],huh:56,hyperspher:83,hypothesi:87,i_1:85,i_2:85,i_3:85,i_4:85,i_n:85,idea:[0,4,21,26,40,43,71,79,81,106,112,119,120,128,129,130,131,136],ideal:[10,11,19,21,24,89,132,134,136],ident:[7,10,23,24,44,45,49,53,55,57,64,66,67,74,80,81,84,85,89,109,112,113,134],identifi:[11,23,44,45,108,128,129],ie2:[34,43],ieee:19,ignor:[11,39,55,78,80,106],iii:[89,137],ill:[11,21,22,50,106,109],illumin:39,illustr:[10,22,23,44,68,85,88,105,108,135],imag:[68,83,87],imagin:[11,122,134],imaginari:[7,45,81],immedi:[40,78,80],immun:44,impenetr:96,implement:[10,34,38,40,78,88,107,108,112,131,136],impli:[7,11,19,38,39,44,45,52,57,62,78,79,80,83,84,85,87,106,108,113,128,130,134,135,136],implic:24,implicit:[11,33,40,42],implicitli:[7,81,88,130,134],importantli:57,impos:106,imposs:[52,84,85,87,126],improp:89,improv:[43,44,48,88,107,108,113,134,135,136],inaccur:[79,82,107,134],inaccuraci:22,includ:[11,12,19,22,24,28,38,39,43,44,58,80,82,85,106,112,131],includegraph:88,inconsequenti:85,inconveni:136,incorpor:[54,134],incorrect:[58,134],increas:[10,23,26,31,43,47,54,58,78,88,95,105,106,109,132,134],increasingli:[90,134],incred:128,increment:[42,81],incur:38,inde:[39,113,130,134],indefinit:87,independ:[24,35,36,42,45,53,59,80,89,107,108,109,111,130,134],index:[15,44,45,67,78,81,107,109,112,134],indic:[10,21,22,23,24,29,39,44,53,58,67,84,88,109,112,128,129],indispens:79,individu:[7,10,16,21,23,71,81,136],induc:[55,57,58,68,83,84],industri:[8,131,137],ineffici:80,inequ:[38,58,83,109],inevit:[59,79],inexact:21,inexacterror:[80,84],inexactvalu:15,inf:[19,23,31,32,34,68,69,70,102,105,126,129,130,134,136],infect:44,infecti:44,inferior:136,infin:[24,83,109,112,126],infinit:[11,19,79,89,111,116,128,135],infinitesim:21,influenc:[88,113,135],infnorm:[68,69],info:131,inform:[11,23,30,39,40,42,46,78,82],infti:[11,19,24,38,39,43,45,55,58,68,69,78,83,102,105,108,109,112,113,128,129,134],inher:[22,106],inhibit:119,initi:[19,23,24,27,36,38,39,41,43,44,88,117,124,125,126,127,128,129,130,132,134,136,137],inlin:129,inner:[7,56,57,78,79,80,81],input:[10,11,21,22,28,36,79,88,107,129,133,134],insert:80,insid:[40,43,44,78,112,134],inspect:[30,85,87],inspir:134,instabl:[0,1,3,6,17,22,45,55,57,85],instal:[12,18,58],instanc:[7,10,19,28,36,38,39,45,52,78,81,83,87,89,112,128,129,134],instead:[22,23,24,31,40,43,55,61,66,67,75,80,85,87,88,89,101,108,113,125,130,132,134,135],institut:131,instruct:[10,18,21,61],int64:[12,15,35,37,63,67,68,71,72,75,76,92,98,102,105],int_0:[24,40,89,96,97,108],int_:[38,40,89,108,112,128],int_a:[24,89,108,112],intadapt:[89,91],integ:[7,11,15,19,23,24,67,78,80,83,106,107,108,112,121,128,130,136],integr:[0,5,23,24,40,43,110,111,112,137],integrand:[0,5,40,89,91,108],integrator_interfac:29,intend:19,interact:[10,87,88],intercept:39,interest:[10,19,20,38,41,57,80,82,131],interf:66,interfer:38,interior:[88,97,113],intermedi:[22,136],intern:[23,57,137],internet:132,interp:112,interpbasi:88,interpbasissi:88,interpol:[2,3,4,5,20,24,30,31,36,38,39,40,52,58,79,84,88,99,105,107,108,110,113,137],interpret:[7,43,55,56,68,78,83,84,134],intersect:[115,122,130,134,136],interv:[19,36,38,39,40,42,45,63,88,89,90,98,106,108,110,111,112,113,122,124,125,128,129,135,136],interview:131,intract:113,introduc:[11,22,40,42,43,44,45,49,53,66,80,83,85,87,106,129,132,134],introduct:[41,56,110,112,137],introductori:[57,80,83],intuit:[55,100,111],inv:[79,84],invalid:129,invari:[106,107],invers:[0,4,11,53,55,56,81,84,130,135],invert:[7,22,58,80,81,85,134],investig:[114,129],invok:12,involv:[7,11,39,44,55,62,80,85,130,134],iqi:136,irrelev:[12,112],isbn:137,ise96:[41,137],iserl:[41,137],ish:47,isn:[0,6,39,85,87,116,134],isnoth:[88,113],isol:135,issu:[10,16,39,54,80,85,129,133,134],item:[24,53,81,88,132],iter:[0,4,38,39,42,49,53,66,79,89,116,117,124,125,126,129,131,132,133,134,136,137],its:[7,10,11,13,14,17,19,21,22,24,28,38,40,42,44,45,52,53,56,57,64,67,79,81,83,84,85,86,87,88,89,106,107,108,109,112,113,115,116,120,126,127,129,132,134,135,136,137],itself:[7,10,15,19,53,57,87,88,89,96,110,112,117],ivp:[0,23,25,26,31,32,33,34,35,36,37,38,39,40,41,42,43],j_3:121,j_m:121,jac:130,jac_is_new:134,jacobian:[119,120,126,127,130,132,133],januari:137,jare:137,jeyabalan:137,jhu:137,job:134,joseph:137,journal:[131,137],judg:[23,89],judgment:[89,128],juli:137,julia:[0,1,2,3,8,10,12,13,17,19,29,49,52,53,55,57,58,59,68,69,70,76,79,80,83,85,86,87,88,96,109,113,128,130,132,135],jump:[23,24,38,39,88],june:137,jupit:52,just:[7,11,19,22,23,24,30,36,38,39,42,43,44,49,52,55,66,68,71,74,77,78,79,80,81,83,85,87,89,96,105,107,112,113,120,128,131,132,134,135,136],justif:134,justifi:[19,38,39,44,134],k_1:43,k_2:43,k_3:43,k_4:43,k_m:119,k_s:43,kai:137,kalman:54,kappa:[11,16,50,55,57,58,59,106,109,112],kappa_2:53,kappa_:[11,22],kappa_f:[11,22],kappa_g:11,kappa_h:11,kappa_r:[11,135],karthik:137,kathryn:137,katya:137,keep:[7,19,21,23,24,43,83,85,87,10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demo notebooks","Chapter 1 (Introduction)","Chapter 2 (Linear systems)","Chapter 3 (Least squares)","Chapter 4 (Rootfinding)","Chapter 5 (Piecewise)","Chapter 6 (IVPs)","Review: Linear algebra","Home","Index","Algorithms","Problems and conditioning","Horner\u2019s rule","Absolute and relative accuracy","Surprising arithmetic","Floating point in Julia","Instability of the quadratic formula","Stable alternative to the quadratic formula","Polynomial roots","Floating-point numbers","Next steps","Introduction","Stability","Adaptive Runge\u2013Kutta","Basics of IVPs","Adaptive RK","Adaptivity at a singularity","Conditioning of IVPs","Numerical IVP solution","IVP with singularity","Using an IVP solution","Convergence of Euler\u2019s method","Convergence of AB4","Accuracy isn\u2019t everything","Convergence of RK methods","Matrix exponential","Predator-prey system","Instability in a multistep method","Euler\u2019s method","Implementation of multistep methods","Multistep methods","Next steps","Initial-value problems for ODEs","Runge\u2013Kutta methods","Systems of differential equations","Zero-stability of multistep methods","Convergence to <span class=\"math notranslate nohighlight\">\\(\\pi\\)</span>","Fitting temperature data","Interpolating temperature data","Householder QR","Instability in the normal equations","QR factorizations in Julia","Fitting functions to data","Computing QR factorizations","Next steps","The normal equations","Overdetermined linear systems","The QR factorization","Conditioning of linear systems","Condition number bounds on error","Timing matrix-vector multiplication","Timing of LU factorization","Timing and flop counts","Interpolating the population of China","Row operations","Using LU factorization","Gaussian elimination","Vectors and matrices in Julia","Matrix norms","Vector norms","Failure of plain LU factorization","Row pivoting","Banded matrices","Cholesky factorization","Symmetric LU","Timing for banded matrices","Backslash for solving linear systems","Solving triangular systems","Efficiency of matrix computations","Linear systems","LU factorization","Computing with matrices","Next steps","Vector and matrix norms","Square linear systems","Row pivoting","Polynomial interpolation","Exploiting matrix structure","<no title>","Adaptive integration","An oscillatory integrand","Adaptive integration","FD at arbitrary nodes","Convergence of finite differences","Comparison of 1st and 2nd order","Roundoff in finite differences","Numerical integration","Extrapolation for numerical integration","Convergence of trapezoidal integration","Polynomial cardinal functions","Poor conditioning in polynomial interpolation","Piecewise polynomial interpolation","Convergence of PL interpolation","Hat functions","Piecewise linear interpolation","Cubic splines","Convergence of finite differences","Finite differences","Numerical integration","The interpolation problem","Next steps","Piecewise interpolation","Piecewise linear interpolation","Cubic splines","Convergence of fixed point iteration","Fixed point iteration","Convergence of Newton\u2019s method","The idea of Newton\u2019s method","Usage of <code class=\"docutils literal notranslate\"><span class=\"pre\">newton</span></code>","Michaelis\u2013Menten fitting","Using <code class=\"docutils literal notranslate\"><span class=\"pre\">levenberg</span></code>","Roots of Bessel functions","Conditioning of roots","Convergence of the secant method","Inverse quadratic interpolation","Using the secant line","The Newton idea for systems","Usage of <code class=\"docutils literal notranslate\"><span class=\"pre\">newtonsys</span></code>","Fixed point iteration","Newton\u2019s method in one variable","Newton for nonlinear systems","Next steps","Nonlinear least squares","Roots of nonlinear equations","Quasi-Newton methods","The rootfinding problem","Interpolation-based methods","References"],titleterms:{"1st":94,"2nd":94,"case":22,"float":[15,19],"function":[10,52,99,103,112,121],"import":[21,42,56,84,111,133],"new":44,ODEs:[0,42],The:[45,52,55,57,80,85,109,117,126,130,135],Using:[30,65,120,125],a_0:40,ab4:32,absolut:13,accuraci:[13,19,33,106],adam:40,adapt:[23,25,26,39,89,91],algebra:[7,80,85],algorithm:[10,53,80],all:[0,40],altern:17,analysi:128,arbitrari:[92,107],arithmet:[14,19],asymptot:78,b_0:40,b_k:40,backslash:76,backward:[22,40,58],band:[72,75,87],base:136,basic:24,bessel:121,block:81,bound:59,bracket:136,broyden:134,cardin:[99,112],cdot:40,center:107,chang:52,chapter:[0,1,2,3,4,5,6],china:63,choleski:73,code:10,coeffici:40,column:81,command:[21,42],comparison:94,comput:[53,78,81],condit:[11,24,27,45,55,58,59,100,109,112,113,122,135],conquer:89,constraint:113,contract:128,converg:[31,32,34,38,46,93,98,102,106,112,113,114,116,123,128,129,132,136],count:[62,78],cubic:[105,113],dahlquist:45,data:[47,48,52,132],definit:[55,87],demo:[0,10,19,22,23,24,38,39,43,44,45,52,53,55,57,58,78,79,80,81,83,85,86,87,89,106,107,108,109,112,113,128,129,130,132,134,135,136],deriv:[40,107],differ:[93,95,106,107,134],differenti:[40,44],divid:89,don:79,doubl:[19,108],effici:[43,78],elimin:[66,80],embed:23,end:113,equat:[0,44,50,55,78,133],error:[22,23,38,40,58,59,89,135],estim:[23,89],euler:[31,38],everyth:33,exampl:80,exercis:[7,10,11,19,22,23,24,38,39,40,43,44,45,52,53,55,57,58,78,79,80,81,83,85,86,87,89,106,107,108,109,112,113,128,129,130,132,134,135,136],exist:24,exploit:87,exponenti:35,express:81,extrapol:[97,108],factor:[51,53,57,61,65,70,73,80],failur:70,finit:[93,95,106,107,134],first:24,fit:[47,52,119,132],fix:[114,115,128],flop:[62,78],formul:52,formula:[16,17,23,40,107,108],forward:107,gaussian:[66,80],global:40,hat:[103,112],have:40,here:44,high:44,higher:[106,107],home:8,horner:12,household:[49,53],idea:[117,126],implement:[23,39,43,79,89,113,129,130,134],implicit:39,index:9,initi:[0,42],instabl:[16,37,50],integr:[89,91,96,97,98,108],integrand:90,interpol:[0,48,63,86,100,101,102,104,109,111,112,124,136],introduct:[0,1,21],invers:[7,79,124,136],isn:33,iter:[114,115,128,130],ivp:[6,24,27,28,29,30,44],jacobian:134,julia:[15,21,42,51,56,67,81,84,111,133],keyword:[21,42],kutta:[23,43],least:[3,52,57,132],levenberg:[120,134],line:125,linear:[0,2,7,56,58,76,78,79,84,86,104,112,128,130],local:38,main:58,map:128,matric:[57,67,72,75,81,87],matrix:[35,60,68,78,81,83,87],menten:119,method:[31,34,37,38,39,40,43,44,45,116,117,123,129,134,136],micha:119,model:130,more:43,multidimension:[11,130],multipl:[60,135],multistep:[37,39,40,45],need:44,neq:40,newton:[116,117,118,126,129,130,134],newtonsi:127,next:[20,41,54,82,110,131],node:[92,107,108],nonlinear:[0,130,132,133],norm:[68,69,83],normal:[50,55],notat:[78,81],notebook:0,now:80,number:[11,19,59],numer:[24,28,96,97,108],onc:57,one:129,oper:[64,81],order:[24,43,44,94,106],orthogon:57,oscillatori:90,overdetermin:[0,56],own:10,piecewis:[0,5,101,104,109,111,112],pivot:[71,85],plain:70,point:[15,19,114,115,128],polynomi:[18,86,99,100,101,109],poor:100,popul:63,posit:87,precis:19,predat:36,prei:36,problem:[0,11,39,42,109,135],pseudoinvers:55,quadrat:[16,17,124,129],quasi:134,refer:137,reflect:53,rel:13,residu:[58,135],result:58,review:[7,80],root:[0,18,45,121,122,133,135],rootfind:[4,135],roundoff:95,row:[64,71,81,85],rule:12,rung:[23,43],secant:[123,125],second:43,seri:128,singular:[26,29],smooth:113,solut:[24,28,30],solv:[76,77,78],spline:[105,113],squar:[0,3,52,57,84,132],stabil:[22,45,55,85,106],stabl:17,step:[20,41,54,82,110,131],stiff:39,structur:87,studi:22,surpris:14,symmetr:[74,87],system:[0,2,7,36,44,56,58,76,77,79,84,86,126,130],temperatur:[47,48],term:[21,42,56,84,111,133],theorem:45,time:[60,61,62,75],transform:44,trapezoid:[98,108],triangular:[77,79],truncat:[38,40],uniqu:24,updat:134,usag:[118,127],use:79,valu:[0,42],variabl:[52,129],vector:[60,67,69,81,83],weight:107,write:10,your:10,zero:45}})