数值计算方法宋岱才版课后答案

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16ᑖ᪆-./0⚪ᑁ34ᦟᩞ7Ḅ⌱9:ᑖὃ<)=⌕?஺ᦑABCD⚪EFᨵᐶIḄJKLMNOPQᐭ᪵ᩩᦪUVᓽL?kᙠm)=n`஺0.48/-0.18x2+o.2x,xe[0,1]<-1.04(X-1)3+I.25(X-I)2+I.28(X-1)+0.5,XG[1,2]0.68(x-2)3-1.86(X-2)2+0.68(x-2)+2.0,xe[2,3]EF4:(1)0.5x3-0.15x2+0.15x,xe[0,1]=^-l.2(x-l)3+1.35(x-l)2+l.35(x-l)+0.5,xe[l,2]1.3(x—2)3-2.25(x—2)2+0.45(x-2)+2,xe[2,3](2)ᦪ!ᨬ#$%
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18ᑖ᪆-./0⚪ᑁ34ᦟᩞ7Ḅ⌱9:ᑖὃ<)=⌕?஺ᦑABCD⚪EFᨵᐶIḄJKLMN!`஺4.èéêᑡë=-2,í=-1,“2=0,*3=1,“4=2Ìᩗᦪgo)=0.5,0&)=0(஽)=0(⌚)=1,"(z)=L5,ᑭᵨUV(4—7)Ï(4—8)᪀⌼(úḄÇÈ⚗V஺஺(“⊈|ü|஺ᑖ᪆-./0⚪ᑁ34ᦟᩞ7Ḅ⌱9:ᑖὃ<)=⌕?஺ᦑABCD⚪EFᨵᐶIḄJKLMNOPᙠÑÒABCEF஺EF4-ý(ஹ)=1,1
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x=x,A2஺஺O=0»஺A%O஺஺A£O=8A஺ಘ=<஺J=%ORA7=361=0,1=0,(P஺J=fo/DOD=285(4j)=£6஺஺(%,)B=41J=0,i=O,஺@A7B=216,ᡠDEFᑮDHI:8,3641136,285CD216F%=222,T=0.95,ᡠDᡠy=2.22+0.95x஺7.UVWXḄVWYZ6[/=/஺"\]^F/_/Ḅ`Iᦪ᝞H⊤

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21ᐜry=a*ឋᓄᓽwxyD10zḄ{ᦪ|=+ᵯ"ᡝ4=F,4=Mg",ᡠD[|4+4N஺$%=4,n=\,00'x=i,XO=”,ᐭ6[Fಘ4⊈஺஺A7ᡈA7=§,A}஺O=AP஺J=Wo/DOkJ=75<ಘ=10MAX,OPA%O=1L875/=,0,/=0,Aᡃ/O="4/஺A7;=33.33A᝕e£:஻"O=51,2275i=o,/=o,5,7.5©433.337.5,11.875Cª4.-5L2275J,F:ᡠDEDFᑮDHI:4=3.708,4=1.972,¬F”3.071,6=0.5056,ᦑy=3.071e°"9.ᵨᨬe\fg°᝞^=஺+%Ḅ²³6[´µᔠDHᦪ஺1925313844y19.032.349.073.397.8ᐜr¶஺+·ឋᓄX=x¸ᑣ[|º=஺+»$᪷=4,஻=1,P3=10MO=xᐭ6[FAὓ஺஺O=¼஺஺°A½O஺஺A¾O=5,

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48ᑖ᪆xyz⚪ᑁ|LᦟᩞḄ⌱ᑖὃ,⌕9஺ᦑ:⚪ᨵᐶḄbSFᙠ:11.594562121.879o010.jk/-4/+4=0ᨵ᪷x*=&,ᵨNewtoni¡x=xm"*r«ᑖ¤¥¦§¨ᐸ஺FজᵨNewtoni«஻x)=x-4x2+4=o,ST:/(X)=4X3-8XO/%x=xᐭ¯°k'T³´VᓽT.7xx4-4x2+4W-4d-8x,·6¸¹º஺=1,»஺/=125,*¼=1.31464,=1.42547619஺x=x"ভঝᵨ“'/À)ᑣÂ=2,ᓽ//ஹoX_4x2+44/X"A2”_8xX,b᪵6¸¹x0=l»M%)=L5,஺(ᓰ)=1.421254,0(x2)=1.4142135஺11.ᵨNewtoniyjkÌ-"0,Í:9*Ḅ,ᵫÎÏÐḄᐹᨵo>ᨵᦔᦪAḄBC¹஺F«஻x=x3_"0,ᡠÒ:rx=3x\ᵫNewtonKrz,ᓽ"rx,᦮ᳮT“#”ÕᔆᓽLᡠ9Ḅ஺

49☢9⏀ᵫQRSRÙ஺=120,ᐭ6¸¹Ú=4»:—=5.1666,Û)=4.94423,0(xj=4.9324415஺13.ᵨNewtoniyjkx஻-a=o,Í:9᪗Ḅ,lim᪗+à9)஺F(1)ᵫá-஺=0,«/஺)=᮱-஺=0,r(x)=""¯°*L**-ã,ᐭ᦮ᳮä+M,åL᪗Ḅ஺lim-=limF=£*)ᵫæᳮ2.æᳮ3.SR…è2!,éê)/஻('*)'+ëᐭìᨬíᓄïL2/*)஺ᡠÒðIñlim"+ò=-lim-ó=lim-…᪗+"…(ô+õöL2/(x*),÷(2)ø/(x)=x"-a,/"[*)=஻(ú)஺/஻(x)=஻("f(ü)ᐭìᓽS9Tð=2ᢚ஺

5014.«/Xᐹᨵ▤ÿ
ᦪ=xr/':1,11/%+/প-/▤ᦈḄ஺ᑖ᪆!"⚪ᑁ%&ᦟᩞ)Ḅ⌱+,ᑖὃ./012⌕4஺ᦑ6789⚪:;ᨵᐶ>Ḅ?@ABCDEF/Z+/x*ᙠ/K0TarlorQRᑮ▤TFUV?WX1YZ[24᩽▲"8`*anO56ឋ018Ḅ9:%
Ḅ⌕1d4ᔜfᔣhᦪjk▣ᦪ஺2d4nopjᩩFᦪ஺3stF/?uvḄk▣ᑖwᡂyzsw{|}~஺Ḅ1k▣Ḅᔜfᦪ?K᝛`1^^W,|=஺2ᔣhḄᔜfᦪxk,|,᱐`7஺3ᦪk▣&k▣Wnop!ᦪ஺

51⚪᪆7⚗+x-x=323«2x+4X+2X=1t231.ᵨ[wឋ|}~If+Z+3X3=2'71-iVx^(3'242wFᐸᑏᡂk▣y&u13¥¦3,ব¨ᐸ©k▣Cᣚᓄ&᝞¤y'71-13ஹf\-11-2'1-1-3-22421=>2421=>0685ஹTτ32,ஹ7I-13,283100TT>,Fᐸ¬®W4wXj-x-3x=22y6²+8&=52831|}~Ḅ¯⚪°&w:T”ᓲ/w´:x«(0.6787,-0.64291,l.1071)7of-0.00222VXA0.4ஹ0.7812501.38162.7µឋ|}~:(3.9965056254¥▲4178¥¶·¸¹º»./=(I.92730,-0.698496,0.900432)7q(1)ᵨ[w®ឋ|}~;(2)ᵨᑡÇᐗÉ[wឋ|}~஺ᑖ᪆"⚪ÊᑡᐭÌÍÎÏ⚪ÐFᙠᨬÒḄ}ÓÔÕ)78wÖ஺

523.Ô4=%,×Ø0,ÙÚaÛ[´ᑮ(2)(2)\422…ainA(2)A=4“4Zi(2)(2)0Üᐸ)…ann,:1Ý/&k▣,ᑣᑁß&k▣;2Ý/&ºᓰák▣ᑣâফß&ºᓰák▣஺(2)(2)(2)(I)(I)16⌕8ä=஺ᡝᓽAç&H=I(I)প01পciij---fiyaUa\\ᵫ/&k▣ᑣÌᓄ&(I)(1)0)Q"O)

53121121r%1%%/I322%%%/22,57ᡠ"ᑏᡂ'卜。/\、1-4%1=62%%5F☢ᐜ=ᓽ:I?”ᱏ:"=ᓽ::#$=%?'(15.+,ᑮ.▣/ḄCroutᑖ7=£஺Ḅ:;<=ᐸ?£@ABC.▣U@ᓫFGBC.▣஺ᑖ᪆IJK⚪ᑁN@ᦟᩞ?Ḅ⌱RSᑖὃ+UVWX⌕Z஺ᦑ\]^_⚪`aᨵᐶdḄefghijklmJ'''2…p=%ᔆ2…ᡠ*-|I/IஹI*=a*-EJ,%:i=k,k+l…%஻/ᔆwxy"1…஻I/LEJo6.mw@{᜻}ABC.▣%1(ᑡ^⌲ᐭZq=/Ḅ<=%2(GZ◤⌕◀

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55ᐜ=7,Y-(I2567312"]#[2'21755055ஹ'7ஹ/%-X02¼3x/H/250XiF22x2VH2x6½¾3>/550X1756"¿¥=Áᓽஹ5#X=(l,2T2)ᓽ@Ḅ஺8.ᵨÅÆᵫ⚪È.▣@B¤CᓰÊ.▣ᵫÅÆÈ:m7ḄLUᑖ2O:

561P2-1ஹ-I3-21Ë-24-216-35,5,ᢥ᯿.▣®¯°±.▣¤²#=2Q=5,40RY,%=4=5,Ì6,/ஹ2X’6ஹ-1%KI-2%0K4%5A☢ᐜ/(="ᓽ:ஹÌ,=38471['5'3'45#:9"UX=Yᓽ:O1-1328Xi_451X~5246Xi3571τ<45>,#ு=%5,4,-3,2(,ᓽ@Ḅ஺9.mᔣÑ*=%4,2,TO(’,ZNL,I”,X\\2oÖ×ØᗓÚÛ஺X14khl7,XØ^y=1110.m/eR"x"@{᜻}.▣à@஻Ḅ·áᔣÑᦪ§ãØ1=ä,ijIIMLæçèḄ·áᔣÑᦪ஺

57ij…{épê=1ëf-.-A@{᜻}.▣¤xH0,ArH0஺¹íî¹ØL=M"=°o"*=°nx=°஺x=ঝðឋ^IL=ভä=MM஺Mk+HL=i“(*+ø□+7ú□+ä=ន+üL஺£H.ýM=lþ)ᐸ?X=(xg,…X")',ᱥM=HL஺=4ᨽ4=஻•4!"#$%WL-(*#஻+1,lk-᩽▲#"h…"…""…113஺;<=ᓝ?limlMI=||x||ᵫᜳ#/?->«I஺12.='ᓃJ,@MLMIL,ML,᜛ভ஺

58CMD(=3,τ/FG=3,(1-2)(1-2]_(5TஹᐜCA'A=[-21A-2IJ=U51ᵫQឋSᦪᱯVᔣXḄZ[\ZA-54'4A-5,]^_`ab0,C#d=Le=fᡠhM"=3,ijk4klmn▣ᡠh:q(fr3஺13.=43e/T"ᙳku᜻wn▣H⊤yn▣Ḅzq{|}ᦪ(1)h1-114,(2)18'஺প"ভ"ভᓽM,=||஺(2)W-=5-/|/(31]||(/|.ᔊ14.=/€/r"klmn▣e…/k/ḄᱯVML=(+…+஺ML•ijk4klmn▣ᦑᨵT=/,ᡠhᨵA'A=A2,

59ᵫke…ekfḄᱯVᵫQឋSᦪḄZ[\Z,/…/ḄᱯV,“+/+…+=ᡠ)஺a0Q=22・2.122・一Z“2ZI“Z/I/2£-2以-s"2”A2+2+22力+=Z所以—2"臼AI力2即H试证明力<-<-0M"ax(/¢,(/f||,4""^/f஻|£¤"ᓽMkMᑴ,◀h#§¨ML.

6016.=4eM”,ᢥn▣ᦪḄ¬ᔣ®¯"°q{n▣±ᦪ஺ᑖ᪆´bµ⚪ᑁ¸kᦟᩞ»Ḅ⌱½¾ᑖὃÀÁÂÃÄ⌕@஺ᦑÆÇÈÉ⚪ÊËᨵᐶÍḄÎ\ÏÐÑyজ|Ó=Ô|,0,ÕÖÕ×=0o/x=0nx=0M1yM”=|ᑄÜᑛIM.஺Mk+y|L=iÂ*+f(+Þ$Ü+IMTNL+IIML஺_C110)poo99)A17.=â71'=199981YCond(4)DCond(B\j-iC஺஺M4=|HLM)=289,qq[5-710ஹ(74105(107æ514974-2105=0,4=0.0045,4=222.9955,105149-AτB,f-9899)"è=[99-looj,CW(5)=||5-'||.||4=3960122

6118.প஺஺3/)=஺஺M4,))(2Cond(AB)6ឋ018Ḅ?@%
Ḅ⌕(1)÷øᵨJacobiýSþ+GAUSS-Seidelᑨᦣឋ஺Ḅ(1)Jacobiᐜ=஺%+஺)!"#-$=o,!᪷'"8஺)<1ᦈ஺(2)Gauss-Seidelᐜ஺=(஺-"0!"|ᯠ/=0,!᪷'஺(3<1ᦈ஺

62ah0defD=0e0(3)678ᦪ:▣<=>ghk)ᑣ=>o0k)o"00ஹL=-d00ஹ-gB஻oD'0-b-cஹU=00-f1°00:ᑖHI!ᢥ᯿LM⌕OPH஺⚪᪆_a0]A1.7'140,9J,஺ḄVWYZ[஻=°஺H=ᵫ⚪^_⌕Zᔛab°,ᓽd“fgh1ij,[4-a0/ஹ/ஹᦑ=4=1H-4…ᕲ=°஺p=pr4g=maxr|a|,0.9gh1uᯠ=0.9h1,vp⌕Mh1,ᓽ10DஹXi'1ஹ-110X02.xyz{r1gJ23,2~3>ஹ~(2)0.50.5V4ஹ0.510.5x102ஹ0.50.51,

63=r1gJacobiᦈGauss-Seidelᦣr2gJacobiᦣGauss-Seidelᦈ஺=r1g✌ᐜᵨJacobi,=»+஺gᢥ᯿:▣᦮ᳮ᝞=Iஹf00Bo0-1Bo=+00100ojஹ஺f120133ᡠ"Pᑡ:A0I2\AE-B\=-120=A5+——=0>033bHp=<ᦪ᪷,ᐸ஺rgh1,ᦑJacobiᦈ஺☢ᵨGauss-Seidel:'00-1ஹ'00-IG=D-L'U=-10000-120J,"Pᑡ:Jஹ<0201|2E-G|=021=r4+1=0002+1,Hp=4=4=0,4=-1P
G=I,ᦣ஺

64r2gᵫ8ᦪ:▣<¡¢y:▣ᦑᵫyᳮ^_=Gauss-SeidelByᦈ஺JacobiᑣLByᡂ¤ᢥ᯿r1gḄz¥Jacobi`Oaᦣ஺-I1X,10-Ix23.xyz{¦U1-5AXJপ3:ᑨ¨ᵨJacobi©Gauss-SeidelHz{¦ḄᦈឋªᦈV«WX¬"BYl°"ḄH஺ᑖ᪆=°⚪±ᑡᐭ³´µ¶⚪·¸ᙠᨬIḄ{»7¼½x¾H¿஺
12—2ஹX,4.xyz{¦r221Àপᑨ¨ᵨJacobi©Gauss-SeidelHz{¦Ḅᦈឋ஺H=✌ᐜᵨJacobi^_=-2'B=D'L+U=-100,Wrl=i:Hp=4=4=4=°,uᯠ஺ᦈ஺!ᵨGauss-Seidel=ᵫÁÂÃÄᩖᦑÆᵨÇÈᐭHᓽ=

65|2£-G|=|AE-rD-£g-C/|=|rD-Lg-2ErD-Z.g-rD-Lg-C/|^D-£g-,[>lrD-£g-/]|t=|rD-Ag||.|[2rD-£g-^]|>"³iÁ0,ᓽ=1°Bgᵪr°"gÓ=°,ᵫÁ=ᡠÔᨵ=Öד°Ø12-2ஹr£>-£g=11221ᵫ:ஹ2212A22Ù,³VPᑡ22-20|[ArD-£g-t/]|=24I=r2-2g=02A-A22ᓽ:2222A:Hp:4=0,4=9=2,ᡠ:P
GI,ᦣ஺1a4a1ÀÛফÝÞX®,x¾Hz{¦5.Ú_z{¦ḄJacobi©Gauss-Seidelᦈ஺ḄVWY஺H=✌ᐜᵨJacobi=23Ẇábrb7g,|2£*-5|==22-4a2=00"Pᑡ=2,Hp=4=4=äᡠ⌕åᦈᑣ:᜛r%g=2Mh1,ᓽ=Óh5஺

66!ᵨGauss-Seidelç:’0-q/oஹ஺0Â10"Pᑡ=êB஺ëB3"‘1஺"4/|=°,Hp=4=0,ᡈ<=4/ᡠ⌕åᦈᑣ=°rGg=4Mh1,gpHh4,ᑣMh5஺;a0ஹ6.:▣r°a\11ÁB¢h“h¢ñ¢yḄòᵨJacobiHz{¦/XiñᦈḄ஺=⌕å¢yoᔜ▤õ»ö÷ᙳᜧÁ0,ᓽ=জ|1|=1>0,,-1<£7<1,@,Hp:üýþ³ᡠÿ&&஺ᵨJacobi:B=D'L+U=02a|ᯠ-=aAᑡ:94=0,ᡈ=!

67P(5)=|a|?6@5(”58ᦈCḄ஺1!⌕E9:oᔜ▤HIJKᙳᜧ70,ᓽজPQR஺<ঝITU7R஺0জ஺஺I——VQW1—VQV12,VWᡠY2ᵨJacobi1IF0-a-a0-a-a8o=D"(L+U)=1-°°~a=-a0-a1-a-a0-a-a02aa|2£-B|=a2a+a2-a2)=(2-a)2(2-2a)=0()ᑡ:a24=%=஺<4=-2a,ᡠ^⌕EᦈC_`a"c)d௃<ᓽ

684=i10.fK2)h0ஹ1"-04=i*:1!k4U,m67U2n,k>Bopᙠ஺᪷sWY᩽▲pᙠḄᐙ⌕ᩩxyz<{|}~ᩭ1ᐸpᙠឋ஺|ᱥ4|=]1ᑡT6"5:"4"TᕴᦈC<᩽▲pᙠ஺[3=T\=fkᧅ஺ফᑡ"412,᜛4=1,ᦣ<ᦑ᩽▲opᙠ஺Ḅ+%”“011.f1%ᑁ+%2=-,1!ḄJacobi>¡Gauss-Seidel>¨©ᦈCᡈᦣTª«¬®>ᦈCḄᐙ⌕ᩩx஺41!¯⊤±ᡂ2▣²<ᓽ[᝞

69✌ᐜᵨJacobi>B„=D'L+U=a"a2l2Iᯠ-=ᑡp50=h·i2%%],o0-%'G^D-L~'u=\a']¸ᵨGauss-Seidel>:஺220஺J42a2iA22|2F-G|==02ana2\0ᑡ:a\\a224_a\2a2\4=0,஺9)=,a\\a22,ᡠ^1©<¨©ᦈC,½ឃI¨©ᦣ஺

701-10-0.25I-0.512.«:I°-°51Ax,JW,oÃÄÅ<ÆᑨÈᵨJacobiÉGauss-SeidelḄᦈCឋ<ÊᦈC<Ë®ᦈCÌÍᑖ᪆Ð7Ñ⚪ᑁÒÓᦟᩞÖḄ⌱ØÙᑖ<ὃÆoÛÜÝ⌕Þ஺ᦑ?«¬ß⚪àá<ᨵᐶäḄ¨åyæ1!<ç±}~èéÓ6êᓰì2▣<ᵫ:ᳮyz½©Ḅ2▣G=3@)õÖö÷ᨵ@øᱯúûü7ý஺1!ᵫþឋᦪḄ

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71Hᵫ-2[ᙍ:2[,
HiJ,᪷bx"c=XAd.e[fxh"”=hl-0[x®—m&:᯿BC/o=&h"+/,
IJB=\-oAq44Ḅᱯs᪷&ᑣBḄᱯs᪷1-⊈&wx-a=y_21l=A-22-l=0{|ᑡCI1ಘ&Hf4=1,4=3ᡠḄᱯsM1-”&1-3⌕ᦈRᑣ11—^>|<120h5[=maxc1-3c<1,HC62d:°<\஺h2[ᵫᳮ
஺ᦈRUVX஺I-<1ᵫH᪆TḄi31,஺d=maxc1-3஺

72p=\-a)p=a)-\P-\-3(Dᡃ஺ᡂ¡᜛Ḅ£ᦪ&ᓄ¦C6f:᜛=3C-1,§¨᝞

73Hᨬª«ᙶ᪗ᓽ3

74rJ,i஺*3.q1஺&஺ᑡ⌕P'4ΰ,ᑣaÏÆÇ4.ÐÑÒᾙ!Ḅ"Ô᪵ᩩÖM£ᦪMx[ᙠDᾙ!ᐹᨵØᑮ▤ḄÛÜÝᦪ஺e=L஺5.q1-1&2ßà஺ÆÇᩩÉ/஺ᑖHáᐸ*Z■ᐹᨵå:#ᐗḄç"#$▣&IJ£=6.êfëᙊ┵Ḅîᙊ/=3.150,ï/T=7.84,ᓫôy_Lᐔ/hhᓽ[õL/=3.14஺>ᵨI"/Mö÷ᙊ┵øù.3J&ᑣ/Ḅúû▲7.3
GùBC“hýþÆÇV=2,&'=஺=ᑣᐹᨵᦪ஺8.ᔣ*=஽,ᑣᕜ+|#+$|%&'ᔣᦪ&)*&)&)*+,+3஽|+.%&'ᔣᦪ&)*&)&)*/01⚪31.5☢Ḅᦪ89:&;<⚗>ᵨNewtonFGH)I;<⚗ḄᦪJKLI;<⚗஺M-210123

75p(x)-51117252.ᵨᨬV/WXK&;Y᝞[=஺+\Ḅ]^_`a5ᑡᦪ8cᔠXD1925313844g1932.34973.397.8h111113.>H)iᦪ஻klপ_nX"q᳝-p(x*)q(x*)-᜛(ᓃ)/2(xjqxḄyᑡz4{|▤~ᦈᑮ=0Ḅ᪷”*஺4.3ឋ/X=(1)ᓃ-*f[S+3)/(3ᵪ)/ᵪX%/▤Ḅ=-1X%|▤Ḅ஺>ᦪ▣ᑖᡂ&;ᓫ5|▣&;¡|▣¢£ᓽᯠ¦ᵨ§Ḅᑖ¨©஺1aa0Xi4a10x12&஺>L¨©ḄJacobi6.«¬¨©01%*nXGauss-seidelnXḄᦈḄᐙ⌕ᩩ»஺

767.¼x*¨/"x=஺Ḅ\½᪷¾¿2,NewtonnXÀÁx=-mஹ,x*40MឋᦈÃᵨnfMᑣÄÅᑮ/▤ÆL஺ÇÈὃ>¨y¼0⚪᪆n=0,1,…20&K¨y3CÍÎ#include#includevoidmain(){doubleIA[21],IB[21];inti;IA[0]=0.18232155,IB[20]=0.0087301587;//ᑭᵨ⌴Ý(A),01IAfor(i=l;i<=21;i++)

77IA[i]=(-5.0)*IA[i-l]+1.0/i;//ᑭᵨ⌴Ý(B),01IBfor(i=20;i>=l;i-)(IB[i-l]=-(IB[i]/5.0)+1/(5.0*i);)஻ßLàáprintf("M&⚪

78

79n\tl(A)\t\t\t\tn\tl(B)

80");for(i=0;i<21;i++)(printf("%d\t%T8.10f\t\t%d\t%-18.10f

81z,i,IA[i],i,IB[i]);

82æçàá:é*D::\prograB\Debug\progra>l.exe*-nxM&⚪inInI00.182321550000.1823215568■10.088392250010.088392216020.058038750020.058038919830.043139583330.043138734140.034302083340.034306329650.028489583350.028468352260.024218750060.0243249055?0.021763392970.021232615280.016183035780.018836924290.030195932690.016926489910-0.0509796628100.0153675505110.3458074050110.014071338312-1.6457036916120.0129766419138.3054415350130.012039867614-41.4557791036140.011229233515207.3455621849150.010520499116-1036.6653109244160.0098975045175183.3853781514170.009336006718-25916.8713352015180.008875522119129584.4093075865190.008253968320-647921.9965379322200.0087301587Pressanykeytocontinue./)iᦪ⊤012345/(x),-7-452665128î177VJᵫðᓃ>ᵨLagrangeFGXK&;íFG<⚗K/஺5ḄñòG஺¨y3CÍÎ#include#include

83voidmain()floatx[6]={0,l,2,3,4,5},y[6]={-7,-4,5,26,65,128},1[6]={1,1,1,1,1,1);floata=0.5,s=0.0;inti,j;for(i=0;i<=5;i++)(for(j=0;j<=5;j++)(if(i!=j)(஻FGöiᦪ

84஻FG<⚗s+=1[i]*y[i];)஻ßLàáprintf("M/⚪

85");printf(zTheresultis%6.3f

86/z,s);æçàá:|ᵨ÷YḄ⌴Ýᓄ01£ᑖ1஺ùú⌕Kûü*ý,.-xlO5ÿ2஺C#include

87#include஻ᦪdoublefunc(doublex)(doublet;t=4.0/(l+x*x);returnt;)voidmain()(inta=0,b=l,k=l,i,j;doubleT[100]={0},s;஻789:Ḅ⌴=ᓄ9:T[0]=(b-a)*l.0/2.0*(func(a)+func(b));do

88{s=0;for(i=0;i0.000005);஻CDEFprintf("HI⚪

89");for(j=0;j

90”,pow(2,j),T[j]);

91printf஻OPQR⌕TḄᑖ⊤W:ḄX=%10.7f

92஻,T[k-ID[\]EF:_ᵨabcRombergfg9:hiᑖ⌕TQRjkl3°C#include#includevoidmain()

93doubleT[4]={3.0,3.1,3.1311765,3.1389885},S[3],C[2],R;inti;஻ᵫHI⚪tᑮTḄXprintf஻H_⚪

94஻[for(i=0;i<4;i++)printff]=%.7f

95”,pow(2,i),T[i]);)i»-»-4-

96fIIIIlZJSZTXXTXXTXZIXZ7*XT*XTXXTXXT*XTSXT*XTXXTXZIXZ7*XT*XTXXTXXT*XTSXT*XTXXTXZIXZ7*XT*XTXXTXXT*XTSXT*XTXXT*XTXXT*XT*Z|SXTXઙJXXTSXT*ZTX\II"):for(i=0;i<3;i++)S[i]=4.0*T[i+l]/3-T[i]/3.0;printf(ZwS[%.f]=%.7f

97”,pow(2,i),S[i]);

98n"V*r%!>*!>*!>v|>^|>%|x^!>*!>K!>v|>^|>%|x%!>*!>*!>^|>*!X*!>*J>K!>\y->fIIIIlZJSZTXXTXXTXZIXZ7*XT*XTXXTXXT*XTSXT*XTXXTXZIXZ7*XT*XTXXTXXT*XTSXT*XTXXTXZIXZ7*XT*XTXXTXXT*XTSXT*XTXXT*XTXXT*XT*Z|SXTXઙJXXTXXT*ZTX\II஻Dfor(i=0;i<2;i++)C[i]=16.O*S[i+l]/15-S[i]/15.0;printf("C[%.f]=%.7f

99”,pow(2,i),C[i]);printf("*******************************************

100஻DR=64.0*C[l]/63-C[0]/63.0;printf("*******************************************

101஻Dprintf஻OPQR⌕TḄᑖ⊤W:ḄXR=%-15.7f

102\R;)\]EF:

103E“D:\prograa\Debug\prograa4.exe*T[11=3.0000000T[21=3.1000000T[4]-3.1311765T[81-3.1389885x«,x*x**>e**xxxxxxxxxStl]=3.1333333St2]=3.1415687St4]=3.1415925MMM'MMXM'MM'MMMMM'MMMMXM'M-M-M-M-M-MMMM'M'M'MM><,CC11=3.1421177C[21"3.1415941MMFGHI⌕KḄMᑖ⊤PQḄRR=3.1415858Pressanykeytocontinuey'=x—y+l,0Yx<0.5yz{X|⚪y(o)=i,}h=0.1,~ᵨEulerஹ⌨ḄEuler789:T஺C#include#includevoidmain(){doubleX,Y1[6]={1.0},Y2[6]={l.0},Y3[6]={1.0},Y4[6]={1.0};inti;for(i=0;i<5;i++)

104X=0.l*i;Yl[i+l]=O.9*Yl[i]+0.1*X+O.1;Y2[i+l]=(Y2[i]+0.1*X+O.11)/1.1;Y3[i+l]=(0.95*Y3[i]+0.1*X+O.105)/1.05;Y4[i]=X+exp(-l.0*X);)X=0.l*i;Y4[i]=X+exp(-1.0*X);஻CDEFprintf(஻Hy⚪

105");printf("Xn\t\tEuler\t⌨Euler\t789:\t

106஻);for(i=0;i<6;i++)

107printfC%.lf\t%.6f\t%.6f\t%.6f\t%.6f

108”,0.l*i,Y1[i],Y2[i],Y3[i],Y4[i]);\]EF:S:\progra*\Debug\progra*5.exe*■-ITXU-Vᵫ11X.n▲Xn1iuleYZ[\⌨EulerZ[^_`Qabc—0.01.0000001.0000001.0000001.0000000.11.0000001.0090911.0047621.0048370.21.0100001.0264461.0185941.0187310.31.0290001.0513151.0406331.0408180.41.0561001.0830131.0700961.0703200.51.0904901.1209211.1062781.106531PressanykeytocontinueᵨNewtonTᑡḄ᪷wᑮ_ᨵᦔᦪ஺(1)஻')=--3ஹ-1=0ᙠ/=2▬Ḅ᪷[(2)஻x)"-3x-/+2=0ᙠ/=1▬Ḅ᪷஺(C)#include#includevoidmain()

109inti=l,Nl,N2;doubleXI[100],X2[100];Xl[0]=X2[0]=2.0;஻ᓫdo(XI[i]=pow(3.O*X1[i-l]+l,1.0/3.0);Nl=i;i++[}while(fabs(XI[i-l]-Xl[i-2])>0.0005);஻i=l[do

110X2[i]=X2[i-l]-(X2[i-l]*X2[i-l]*X2[i-l]-3*X2[i-l]-l)/(3*X2[i-l]*X2[i-l]-3);N2=i;i++[}while(fabs(X2[i-l]-X2[i-2])>0.0005);஻CDEFprintf(஻H⚪

111஻);printf஻পᓫ

112஻;for(i=0;i<=Nl;i++)printf7f

113",XI[i]);printf஻ᑭᵨᓫOPᨵᦔᦪḄḄ᪷x=%6.3f

114஻wXl[Nl-l];r^!**!**!**4**1**1**X**1**1**1**>1**1**1**1**>1**!**!**!*«1**1**1**l**!**!**1**!**!**!*I1JIjIII\xjxxjsxjvxj%xjxxj*xp*xjs

115");

116printf("(1)Newton

117");for(i=0;i<=N2;i++)(printf(/z%10.7f

118”,X2[i]);)printf(஻ᑭᵨOPᨵᦔᦪḄḄ᪷x=%6.3f

119஻,X2[N2-1]);)\]EF:

120r/\-0.00222ஹX,'0.4ஹ10.781250X21.3816¢.£¤¥ឋ§3,965056254,ஹ7.4178,¨©ªX’=(1.92730,-0.698496,0.900432)'1ᵨ¬®¯°¥ឋ§[2ᵨᑡ±ᐗ³®¯¥ឋ§஺MATLABclear;clc;D=zeros(3,4);E=zeros(3,4);A=[-0.00222;10.781250;3.9965.56254];B=[0.41.38167.4178]';C=[AB]D(l,:)=C(1,:);E(l,:)=C(1,:);fori=2:3

121forj=l:4D(i,j)=C(i,j)+C(l,j)*(-l)*C(i,1)/C(1,1)endendE(2,:)=D(2,:);forj=2:4E(3,j)=D(3,j)+D(2,j)*(-l)*D(3,2)/D(2,2);endB1=E(:,4);x3=vpa(Bl(3)/E(3,3),8);x2=vpa((Bl(2)-E(2,3)*x3)/E(2,2),8);xl=vpa((Bl(l)-E(l,3)*x3-E(l,2)*x2)/E(l,1),8);x=[xlx2x3]EFᵨᑡ±ᐗ³®¯¥ឋ§ḄḄ᪷¸:

122X=[1.9273000,69849600,.90042330]'430ஹ'24ஹ34-130-24L§Ḅ¹ᵨS0R§I஺-14ºᑮ¸X*=3,4w-5'஺C#include#includevoidmain()(doublexl[6]={1.0},x2[6]={1.0},x3[6]={1.0};doublew[2]={l.0,1.25);inti,j;printf("H¹⚪

123");for(i=0;i<2;i++)printf"»ᦪkw=%f

124஻ww[i]);

125printf($z\txl(k)\t\tx2(k)\t\tx3(k)

126");for(j=l;j<6;j++){xl[j]=xl[j-l]+w[i]*(24-4*xl[j-l]-3*x2[j-l])/4.0;x2[j]=x2[j-1]+w[i]*(30-3*xl[j]-4*x2[j-1]+x3[j-1])/4.0;x3[j]=x3[j-1]+w[i]*(-24+x2[j]-4*x3[j-l])/4.0;printf7f\t%.7f\t%.7f

127”,j,xl[j],x2[j],x3[j]);)\]EF:

128c:*D:\prograA\Debug\progra>8.exe*-nXSA^»ᦪkw=l.000000xlx2x315.25000003.8125000-5.046875023.14062503.8828125-5.029296933.08789063.9267578-5.018310543.05493163.9542236-5.011444153.03433233.9713898-5.0071526»ᦪk“=1.250000xlx2x316.31250003.5195313-6.650146522.62231453.9585266-4.600423833.13330274.0102646-5.096686342.95705124.0074838-4.973489753.00372114.0029250-5.0057135Pressanykeytocontinue