数值分析(宋岱才版)课后答案

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10Ḅ>?@ABCD*ᑖEFᐭNewtonNewton@H/(0.05)=1.05126.11.O⌕56/(x)=cosx,xT0UḄVWᢥYZ[\hᑖ^Ḅ_ᦪ⊤*bᢥcឋ/0xeḄcosxḄ஺efhghᜧjklmᐸopqrḄst-uv_2_?10"஺ᑖ᪆⚪ᑁ"#ᦟᩞ&Ḅ⌱()ᑖ*ὃ,-./0⌕2஺ᦑ4567⚪89*ᨵᐶ<Ḅ>?@ABCD*Fᐭz⚗*ᓽ@26}40.02஺12./(x)ec2"+2[q,@*ᵨLagrangez⚗Ḅm*m:ᱯz⚗f2"+2(£]R(x)=/(x)-”2,(x)=2஻+2)!ᵨ(X)஺ᑖ᪆⚪ᑁ"#ᦟᩞ&Ḅ⌱()ᑖ*ὃ,-./0⌕2஺ᦑ4567⚪89*ᨵᐶ<Ḅ>?@ABCD*ᳮ2Fᐭz⚗ᓽ@2H*ᙠ-.஺13.2-uv3Ḅh⚗“(X),ᐸ¡”(-1)=9,(-1)=137(1)=1W,(l)=-1oᑖ᪆⚪ᑁ"#ᦟᩞ&Ḅ⌱()ᑖ*ὃ,-./0⌕2஺ᦑ4567⚪89*ᨵᐶ<Ḅ>?@ABCD*ᡠ2h⚗#H(x)=a+ax+ax2+ax3,Fᐭᩩ¨*ᓽ@2H:0l33//(X)=X3-4X2+4X«14.2-uv4Ḅh⚗p(X),ᐸ¡P(0)=«(0)=0*P(1)=P/(1)=1,Pফ=1஺ᑖ᪆⚪ᑁ"#ᦟᩞ&Ḅ⌱()ᑖ*ὃ,-./0⌕2஺ᦑ4567⚪89*ᨵᐶ<Ḅ>?@ABCD*ᡠ2h⚗#ᑖ᪆p(x)=a+ax+ax2+ax3+ax4,Qt234Fᐭᩩ¨*ᓽ@2Hp(x)=|?(x-3)2o15.5_ᦪ⊤012300.521.5஻¯)(1)ᙠ°±ᩩ¨/²=0.2,/(3)=-1³2´᪵ᩩ_ᦪS(X)·(2)ᙠ°±ᩩ¨/஻(0)=-0.3,/஻(3)=3.3³2´᪵ᩩ_ᦪS(X)஺ᑖ᪆⚪ᑁ"#ᦟᩞ&Ḅ⌱()ᑖ*ὃ,-./0⌕2஺ᦑ4567⚪89*ᨵᐶ<

11Ḅ>?@ABCD*Fᐭ᪵ᩩ_ᦪ*ᓽ@2H*ᙠ-.஺0.48x3-0.18x2+0.2x,xe[0,l]89#1x=J-1.04x-l3+1.25x-l2+1.28x-l+0.5,xe[l,2]50.68x-23-1.86x-22+0.68x-2+2.0,xe[2,3]0.5x3-0.15x2+0.15x,xe[0,l]2jx=--1.2x-13+1.35x-12+1.35x-1+0.5,xe[1,2]1.3x-23-2.25x-22+0.45x-2+2,xe[2,3]

12ᦪᨬ!V¸Ḅ?7⌕2(1)¹ᵨᨬ»¼½2¾ᔠÀc஺(2)¹Ácឋ_ᦪÂᓄᡂcឋ_ᦪ஺¼¸ÅÆÇḄÈÉcឋÀc¾ᔠ(ÊಘᧅভÊ0)஺஺(}3M=(஺ಘᨔ0Ê(Ïᵫ(}j=0i=03Ñ஺)=£ÓÔ)஺Ô)*ᵯf'=£o)WCyᵯFGজ,(KWyi=0i=0´¸7⚪C᪆1.஺°(x),@(x)…஺,i(x)…ÙÚÛÜ0,1ÝÞßᩗ᜛(}=âḄᨬã⚗äᦪ#1Ḅåæh⚗çᑡ*ᐸ&0o(x)=l,2*x஻(x)dxê°|(x)࠷)஺ᑖ᪆⚪ᑁ"#ᦟᩞ&Ḅ⌱()ᑖ*ὃ,-./0⌕2஺ᦑ4567⚪89*ᨵᐶ?@ABCD*ᙠîï45689஺89#(x)dx=12·.(x)=x-2;'Ü0,^^03//\263ó3=%-1+ᔊ஺2.ᑨp_ᦪᡈ(x)=l*/(x)=x,*ó(x)=%2_,ᙠÜ-1,1ÝÞßᩗ᜛(x)=låæ*b2.(}ᐸᙠÜ-1*1ÝÞßᩗp(x)=løù(X)*0")*ᡃ(û)åæ஺ᑖ᪆⚪ᑁ"#ᦟᩞ&Ḅ⌱()ᑖ*ὃ,-./0⌕2஺ᦑ4567⚪89*ᨵᐶ<Ḅ>?@ABCD*ᙠîï45689஺89#5

133.mO_ᦪüý…஺þ)Ùᙠa,bÞßᩗ᜛(x)åæḄ_ᦪü*ᑣ(x),ᵫ(x)…0,*)ᯠឋᐵḄᦪ஺ᑖ᪆⚪ᑁᦟᩞḄ⌱ᑖὃ!"#$⌕&஺ᦑ()*+⚪,-ᨵᐶ0Ḅ1234567஺4.89:ᑡ==-2,᳝=-1,x=0,x=1,%=2Aᩗᦪ0(x())=0.5,23

15A(x)=XÌᐭGHt(஺▂=£জè(%,)%)=5é)=(o஺0)Nটo(%")=75ê”)=஺ì)")=11875,(஺í=Z0,ᡃ(%,)y=3333(°j)=èটo(%,)y,=51.2275K<=0/=0ᡠs3stᑮsvbc[5,75][A>]=p333],Rt4=3.708_7.5,11.875_|[Aj|_51.2275_4=1.972,Ìó&t஺=3.071,8=0.5056,ᦑbcy=3.07le°s°56l9.ᵨᨬª«¬&ö᝞y=a+bx2Ḅ÷øGHùú^ᔠsvᦪ\஺192531384419.032.349.073.397.8yRᐜ¶y=a+s2ឋᓄdX=f,ᑣæH¾y=a+/?x,UV஻?=4,஻=1,0oÛxÜ="஺ýÜ=xÌᐭGHtÛèಘ=ὡ0oÛkÛ=,Ü=5Û஺éÜ=ÛᡃaÜ4GoÛÿ
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3X=X3-X-5,¼Q"|=%*-5Ñᑖ᪆ÔÕ¼QḄᦈ4ឋË⌱Õᦈ4ᨬÙḄ¼QÚᐹᨵÛ°ᨵᦔᦪ²Ḅ´Ü᪷஺u1wÝÞ5ᨵ᪷ßàTE2,3I,ᵫ89?஺uxw=^2x+5,áâ:“ã=2.302x+5ᙠᨵ᪷ßàE2,3Iᑁ,uxw|

33(1)“é=3+10%—20=0ᙠßàE1.5,2IᑁḄ᪷;(2)/(x)=/-3x-l=0ᙠ᳝)=2▬´Ḅ᪷஺ᑖ᪆7ëj·⚪ᑁìTᦟᩞïḄ⌱ð1ᑖ%ὃÑòóô⌕஺ᦑörÚ÷⚪øù%ᨵᐶûḄÄü?ýÃþ%ᙠ¿örÚøù7(1)x*=1.5945621஺(2)x*a1.879஺ᜩ!᪷4Mᑖ$%&'10./-4*2+4=0ᨵ᪷=j,ᵨNewtonᵨf'M()*+ᐸ-.஺/0জ2ᵨNewton)3/!4/+4=0,560fl(x)=4x3-8xo&ᐭ<=%&>?0ᓽ600(x)=x_/_BC+4,DEFG*f'\)4X3-8Xx°=\,HI%&:K/)=1.25,0(᳝)=1.31464,OP)=1.42547619஺ঝ2ᵨ%&>?RS4-TUV)ᑣX=2,ᓽ"Z,_2[S+4.\᪵fE)4x--8xEFGx°=lHI%&00(%)=1.5,^(x,)=1.421254,^(,)=1.4142135»x11.2ᵨNewtonca=0,efghḄ%&>?)jᵫlmn#pḄᐹᨵrsᨵᦔᦪvḄwxG஺ᵫNewton%&>?}!=஽!41)ᓽ0/03"X)=x'-4=0,ᡠ|0f'(x)=3x2f'M^)=-K᦮ᳮ60=lᓽᡠgḄ%&>?஺xxf'(x)3x☢g“p)ᵫ5)lKa=120,&ᐭ%&>?°(x)=x-S)EFG=4HI%&0°(%o)=5.1666,0()=4.94423,0(%,)=4.9324415஺13,2ᵨNewtoncx"-a=0,efg᪗'Ḅ%&>?)jglim!)஺/0(1)ᵫx"—a=0,3/(x)=x"—a=0,f'(x)=nx"-'.<=%&>?0!)&ᐭ᦮ᳮ0᪗Ḅ%&>?஺4+1=x*f'M[BInJn

34ᵫᳮ2.ᳮ3.50=஽+T,60(x)=X!1&ᐭZ?i,2!rwᨬᓄ0ᐭ஺2/(%)(2)ᡠ|¡01¢£¤■=-lim'”=lim-=4Z4,§¨0-©-4[GxJ=ª2/(x-)f(x)=xn-a,/)(x*)=஻(T¬஺/஻(£)="(“—1)(®”[&ᐭZ?ᓽ5g614.3/(°)ᐹᨵ▤²³eᦪ,/(x*)=OJ'(x*)#0,¡%&>?X=_______(xj_____¶▤ᦈ¸Ḅ஺xᑖ᪆0ºc»⚪ᑁ¾ᦟᩞÁḄ⌱ÃÄᑖ)ὃÆÇÈÉÊ⌕g஺ᦑÍÎfÏ⚪-.)ᨵᐶÑḄ\Ò5ÓI¡)ÔÕ0/■(%+/■(%))ᙠ஽×ÈTarlorÚÛᑮ▤)Ý>?Þß\Kàá஽)g᩽▲limä,åXK஺Z!X

356/7ឋ,-9Ḅ:;/!»æḄÒÏ⌕g(1)çgᔜéᔣëᦪí▣ᦪ஺(2)çgïðñᩩᦪ஺(3)óôÇ\õöḄí▣ᑖ/ᡂLUú?jó/ûü஺»æ2ýþḄ×>?প▣ḄᔜᦪM||=maxMJ,MmaxJ6Jmax(TA)஺11“8">1'1111,114ᨴi=lফᔣ!ḄᔜᦪN=maxkᧇflx1111001m4n111,1i=l(3))*ᦪ▣+,-▣./01234ᦪ஺9:;<⚪>᪆7x+x-x-3t231.ᵨBCDEF>GឋIJK2%+4%+2O=1-x+P2+3%3=21f7>Rᐸᑏᡂ▣VW+2,X,ᐸYZ▣[\]2^ᣚᓄ+᝞b(71-13ஹ‘1-11-2ஹ1-1-3-2VW242,Rᐸjkl.m>1=>2421=>0685ஹe1132;J1-13o஺஺pq33%eᓰe3ᓰ=2.,,kIJKḄs⚪t^+>u6Xo8X=5>wxz(0.6787,-0.64291,1.1071)""-0.0022'0.4ஹ2.z{GឋIJK|}~>10.781251.3816ஹ3.9965056257.4178,x*=(1.92730,-0.698496,0.900432)'஺

36(1)ᵨBCDEF>lGឋIJKo(2)ᵨᑡᐗDEF>GឋIJK஺ᑖ᪆:⚪ᑡᐭ⚪RᙠᨬḄJz>஺44=(%).eব0,eBCDEFwᑮ,ᐸ((2)(2)ஹa22…ain:A"=..............ফফa)nn(1)¢4+,-▣ᑣAব¤+,-▣;(2)¢A+,¥ᓰ¦▣ᑣAফ¤+,¥ᓰ¦▣஺(I)(1)¨⌕.বᓽ«¬+=J"ᵫUyUjiUijUijnii\uijCl[j(I)Cl\ja\\A+,-▣ᑣWᓄ+(1)প<|)(l>(1)Uj\(t)0)(I)ফaji-------j\=ciji--------------(^a\i=Q[-m^au=Qᡝa\\a\\µ஺¶ᳮ«(2)o(21(414.ᨵIJKi=6,ºR*ᦪ▣ᑖ>ᡂe»ᓫ½b9¥▣e»93J2,¥▣¾¿oᓽ4=À஺ᯠᵨÂḄᑖ>>lIJK஺(21(1W11H\1U13>RAᑏᡂLUḄVWᓽu32=/,1,ᑭᵨ▣ḄÇFU22UJ22)ஹ/31132Uzg1_o——1.3333w"=/3l=5'Wll=2>஻12=஻13=1'/=5'"22=5'஻23=/1/33=53221rᡠÉA«ᑏᡂ:132122,yy«4,|b☢>lIJKᐜ>ᓽ:,,>w:PJ->ux=y,ᓽ:

3771]/x.'*Ï4>wX=Ð1,1,1ÑÒ஺7272X=423/UJJ2I/5
প5.ºÓᑮ▣AḄCroutᑖ>A=LUḄÖWᐸL+b9¥▣U+ᓫ½9¥▣஺ᑖ᪆×3:⚪ᑁÙ+ᦟᩞḄ⌱ÝÞᑖὃºàáâ⌕m஺ᦑ¨z<⚪äåᨵᐶçḄ¶è«é\êël.,/=1,2..-H;M,.^,j=2•••«,,ᡠÉlj=aik-l](k-1\l=aI3=k,k+1…n,u=y~ïj=%+i…”஺=1IkNE>6.L+ò᜻ôb9¥▣Ð1Ñᑡ⌲ö÷ᐭm>LX=/ḄÖWoÐ2Ñøm>J◤⌕úûöÇ◀F?XiÐ1Ñ,ᐸ//o(i=l,2n)oþL=+%5;fA-1fklkrXj/OQ\>øIJK«Éwᑮ:XiKk=(2,3....n)oXi=-j-l\\kkT◀஺Ð2Ñöᦪ+:1)+1]+“=7.ᵨ᪷ᦪ!▣A$%&'!▣,(ᵨ᪷)A*ᑖA=LEᓽ᝞./0:241-10ஹ/),11112113114113-1021i2222C32142,ᢥ᯿!▣>?@A!-1-15231C32஺3333r34<0024,41b42043447447-⚪)…஺▣$B᦮ᳮEF=2,"=,I223222"2

38,X-xVT13JKz5x=y,ᓽ~T-REX=(1,2,-1,2)2ᓽḄ஺'2-1'6'8.ᵨMN-131-20ᵫ⚪*P!▣Q$RᓰT!▣)ᵫMNPUAḄAUᑖ:2-1-13V,ᢥ᯿!▣>?@A!▣$-241)B*E0=2n15A419540஺2=5'A=-yo=pW=-Xm=5,Y=Z)[=-2,=-i»r2/\2y'6ஹ.☢])ᐜLY=6,ᓽ--%)E84711Y='5'3’45-2%0%“=5)`K)ux=Y.ᓽ:

39'3ஹ1--28Xi45,EX=b5,4,-3,2c)ᓽḄ஺1%2546a3315711<45>9.Uᔣf1=b42-U0c')iM,kl|n஺=10>=l7,=%/2=MLmax|x|=Hr§WM2V?bc11010.UAeR"*"~᜻!▣)ᧇ|R"Ḅᔣfᦪ)'k=MM)R"Ḅᔣfᦪ஺:জ~ᖹcb=|2•••A~᜻!▣$xw0,Ax஺0||x||-1|^||&=>=Ax=x0oঝឋ᪷⊈=1.ii1=1ᙬ஺ঞ||x+y||2|Abx+ycHAx+Ay|¤+|¥|=kb+¦§11¨kk©lᐸ«….4)᯿M§L஺\M7§b=¬kl4®'k஻°⇟²’´µ¦¶?2EkLWWk)¬`·k[᫂L)´µ¦¶¹᩽▲E§g½k¾ᑣMÀḘÂkkkôµᜳEᜐM=M஺12.U[ÆÇc)i¦)lÈk஺bÉMb=r^gx£|aJ=3)Mlk¬x2|aj=3)||A||=^AmaxbA7'Ac.2S1_?VI_2ஹS5-4ஹᐜA7A==,ᵫÏឋÐᦪᱯÒᔣfḄPÓ*P:1-21A-21J1-45Ç

40ττZ—515,ÕÖ¾0×Ø0,EÙ=12Ù=9,ᡠÛ¦,=4=3,|Ô-§4ÜA$%!▣)ᡠÛp(x)=||A||=3o213.UA,Be/T*"ᙳ~᜻!▣)k|⊤ß!▣Ḅàáâᦪ)পk1§lÇফlA'-B'hkIMIMM஺পåE||W§|AæM2ç/ᓽM[$=PIIফ@-51=èé4k||43-8)5$41k¾êkè1஺14.UAeR"ஹ'$%!▣))ÇI22…ÙAḄᱯÒë)=(·+ì+“+î)Ç஺ÜA$%!▣)ᦑᨵA7=A,ᡠÛᨵAZ=A2,11"À»=|)=1ᵫÇI/Ù)…Ù4ḄᱯÒë)ᵫÏឋÐᦪḄPÓ*Pñ)ò)…ò£ḄᱯÒë)(4K+/Ç+…+ᐗ=ᓡõ஺Cl\\Cl\2Cl22AA=[஺ᔊ஺2nf=lᡠÛ/+%;+•••+a=11ù=11ú஺iai2j=lr=l1=1ᓽMii.=(û+ü+“+/y஺15•U",ýᔙMbMMW=%max(A2A)A7)=||^||-max(A7)="ÿ',ᓽMIHWI◀ᓰ

41MIHIWMW%16.AwR"*",ᢥ▣ᦪḄ$%&'()*▣ᦪ஺1=1j=lᑖ᪆./0⚪ᑁ34ᦟᩞ7Ḅ⌱9:ᑖὃ<=>?@⌕B஺ᦑDEFG⚪HIᨵᐶLḄMNOP&'QR©||x||=px||>0>Z[\Z]=||Ax||=g=4x6=x0஺ঝ=abᑘ=᪛ebMHLঞ|k+4=m'+>)1=o+4pಗ+r|=||s+3|u஺(7]0ஹ(100QQAz.{57'}9998'Bᙊ”)“(஺஺ম஺4*(—71oA஺஺p={.|ᓽ=289,1==(5_/7{{474105ஹCond^A\=V4n
47=222.6058A"=7ᔆ105149,U074-2105{_=0,=0,4=0.0045,4=222.9955,105149-22H;ு஺஺஻"2=|•=39601஺18.&'1Co஻d4=Co஻d472CondCondA-CondSB
o&'1ᵫ$%NCondSA'^4)'1•|AT|=|•|A[H/r[M|=Co஻dA,ᓽ1ᡂ£஺2Cond¥=¦[.e=§-¨|.|e©§1|ª|ᡃ'1=¬-'I•§-11•|=CondSA
Cond஺

42)/7ឋ,-9Ḅ>?)0®ḄMG⌕B1¯°ᵨJacobi¶·¸¹GAUSS-Seidel¶·¸ᑨÀÁᦣឋ஺0®°ÄÅḄÆÇÈÉপJacobi¶·ᐜBÌ=஺4+{/,ÎÏÐ|=0,Î᪷Ò0Ð<1ᦈÁ஺ফGauss-Seidel¶·ᐜBG=£>-4/t/ÎÏ|Ú/=0,Î᪷ÒpG

43¶·ᦈÁ஺&'1✌ᐜ°ᵨJacobi¶·¸üý80=£>TA+U2ᢥ᯿▣þ¸᦮ᳮ᝞:ஹ0000-1,ᡠᑡ:=+01000Jஹ12053/201|-=-12+,+!=஺,#$:%&'ᦪ᪷*ᐸ,-.0/<1,33~3ᦑJacobi78ᦈ:஺☢<ᵨGauss-Seidel78E:0-1ஹG=D-L't/=-1100=00-1*ᑡ:J10J20-I01\AE-G\=0/1=K-K+1=0,#$L4=4=0*&=O10G=1,P00A+1ᦣ஺2ᵫTᦪU▣&WXYZU▣*ᦑᵫZᳮ[\LGauss-Seidel78OZᦈ:஺]Jacobi78ᑣ_OZᡂa*ᢥ᯿1ḄeEfgJacobi78&Pᦣ஺f8-13.kZelm210ᑨoᵨJacobipGauss-Seidel78#qelmḄᦈ:ឋ*sᦈ:*tuvx°=0,0,0',y-.z““—/}YICT?Ḅ#஺ᑖ᪆L⚪ᑡᐭ⚪*ᙠᨬḄlk#஺4.kZelmᑨoᵨJacobipGauss-Seidel78#qelmḄᦈ:ឋ஺#L✌ᐜ<ᵨJacobi78E[\L0-22ஹB=D'SL+U
=1-10-1=-10-11:01-2-202-20,

4422-2\AE-B\=1A1=23=0,#$L4=4=4=°*ᯠ஺<1,ᦈ:஺022A<ᵨGauss-Seidel78E:G=SD-L
-'uKᵫyO-L¡¢'ᩖ*ᦑ¤ᵨ¥¦8ᐭy#*ᓽ:|2£-G|=|/L£-D-Lf't/|=|D-Lf'/l£D-L-D-L''t/|=|0-ᑗ00--4=|0-஺1ª0-"-”*®0,ᓽ:|D-L-'|.|¯2D-L-t7}|=0>ᵫL|஺-Ó,0*ᡠ±ᨵL¯4஺-+஺}=°஺’1ஹ'22-2ஹᵫLO—=11*¯AD-L-/}=221»Wtᑡ*L21J24A
22-2o1=o,#$L4=0*4=4=2,ᓽL¯2Q-L-Uj=%21=2-222-2222Z222ᡠLpG>l,Pᦣ஺5.»\elmf1"¼½}=1*W¾¿XÅ*k#qelmḄJacobi78Ep14almফGauss-Seidel78Eᦈ:ÆaḄtvÈ஺#L✌ᐜ<ᵨJacobi7EL&=஺4+£/=1ÉÊ/°f*"4஺0JᑡL|_=jL=ᑖ_4/=0,#$L4=4=±267,ᡠ⌕Öᦈ:ᑣ<-.L஺Ì=2Í<1,BPL|a|<—o<ᵨGauss-Seidel78ÐLG=SD-L\'U=1Jfo-a}fo-a}[o0)(o4a2)ᑡL\AE-G\=^-SD-Ly'u\=^^Ê2=0*#$L4=°Kᡈ4=41,ᡠ⌕Öᦈ:ᑣ<-.LpG=4a2|

451a06.gØU▣a1aWOÙYZḄ*ÚqÆᵨJacobi78E#elmV2V2ஹ0bAX=bÆÙᦈ:Ḅ஺gØL⌕ÖYZ=ᔜ▤Þßàᙳᜧ0,ᓽLজ|1|1ு0,ঝa=1-1>0,a1a0—1<஻<1,ঞ—a%஺,#$LOè<"+,/ᡠé:11a1aOY,”Y0a10-a00-a0<ᵨJacobi78Ð:5஺=/TL+U=-a0-a-a0-a0-a00-a020ᑡLplE-8o|==2ëO/=0,#$:4=0,ᡈ%=ì஻*aQ0a2Pí=\a\<1*î⚪ᡂa஺1a117.gØU▣a1aWOÙYZḄ*]Jacobi78E±Wߟ—0,©=l-a2>0*aaa1=2a3-3a2+l=2«2(a-l)+(l-a)(«4-l)=(a-l)2(2a+l)>0,#$L——/ᡠéL——<஻<1஺22-a0-a-a<ᵨJacobi78ÐL&=QTL+U=-a-a0-a0-a-a02aᑡL|/£-/|=a2a(2—+Q4—Q2)=(4—4)~(%—2a)=0#$:aa2ᡠ⌕Öᦈ:ô-.Lh&<1,ᓽLᔣ

46ஹ0}0io.4÷2,gØøAJ0,ùW4=11Æ*limA/_úᙠ஺ᦇO»816J2)2>#:᪷üé᩽▲úᙠḄᐙ⌕ᩩᩭᐸᙠឋ஺(1)ᑡWE-4|=!p#Aj=gমlpd\20✌ᐜoᵨJacobiLMN8஺ᑐstan’0Cl\i6ZH10ஹv஺21a210Cl11)Ia22£12.2ᑡ!y£-z{=|_~2=0,D:᜛#99=a21஺11஻22A஺2200—qoᵨGauss-SeidelLMN:G=(D-Ly'u=00a\2a2\0a2200~a2la\\a22a\\a\2\^21a\\00)0a\Ia22)12|Aᑡ!|—G|=஺1௃஺22=o,D!4=0,4=4ᔳᡠy4௃2%1“110220

47!p#G9=1XWXᦈ*1WX;ᦣ஺12.\234_o251_05v=o0ᑨᵨJacobiGauss-Seidel..X20-0.5LMDE234Ḅᦈ*ឋᦈ*_LMᦈ*¡ᑖ᪆!¤¥¦⚪ᑁ©ªᦟᩞḄ⌱¯°ᑖὃ0²³´⌕µ஺ᦑ¶\]·⚪¸ᨵᐶ»ḄW¼½C¾c!¿ÀE23ªÁÂᓰÄe▣ᵫᳮ!0஺41X23SORLMᦈ*É஺Êtᦈ*Ë஺13.ÍCGauss-SeidelLMNḄLMe▣G=#OUÏÐᨵvÑᱯÓÔÕ¥Ö஺C!ᵫ×ឋMᦪḄÙ!Ú=44…%Ëܪ!W=|#஺-ÝÞß=0à!g-L9ârO,ᡠy|u|=o,Ëܪuª{äÂe▣ᡠy!@=4æ…çÏÐᨵvѪÖ஺14.è234#2?Z9éê#ëÁ³ìX#°9,ᵨLMï—ð=ñò9vë#4Þò9—69µDE234X#19ëḄôÔö÷LMïᦈ*Z#29஺ô´ÔXᦈ*øùᨬ¡D!ᵫû4=#j᪷ý/+19!=#l-£yx"᯿x""=+/,MAAḄᱯ᪷ᑣ6Ḅᱯ᪷1—!τ.
A.2ஹ2..%&ᑡ—(==)—2--1=0,,-4=1,4=3,I1X-1ᡠ!8Ḅᱯ31-3,41-3ᗂ⌕7ᦈ9ᑣB;<=᜛8=max{|l—D,|1—3EF1,,GHI!KDFL,-0FyF2஺O|l-3ty|Fl32ᵫRᳮGUVᦈ9WXUY஺|1-D<1ᵫ,᪆[\Ḅ]7_᜛5=max{|l-a|133஺

48,ᨬVcdᙶ᪗ᓽ30-1=1-জ,-ᑓ=,ᦈ9ᨬY஺2

49@AB⚪jklk3ᑖᐳ30ᑖ1.ᵨpqr4+1stu/'=X3-/%1=0Ḅ᪷⌕ypqzᑡ{|ᐹᨵtᦈ9ᑣ=ᓽ஺2.yᵨrSOR,ឋtuI=8஺ᩩRᦣ஺3.A2=M1°1⌕yliM=0,ᑣa____________m0,0.52J—4.{Ḅ᪵ᩩ3ᦪsxᙠ[a,{ᐹᨵ¡ᑮ▤Ḅ¤¥¦ᦪ஺1,a~]15.A=§஺ᩩA!ᑖ,¨ᐸªLᐹᨵ¬ᐗḄ¯°▣5______________6.²-³ᙊ┵Ḅ¶ᙊ<=ᔆ*=3.150,¹º=7.84,ᓫ½cm¾¿À*=3.14஺ÁᵨÂ3ÃÄᙊ┵ÅÆÇ=1ÀᡝÉᑣvḄËÌ▲37.ÎsÆÏ£4=2,Ñ4஽=0,£Ó$=1ᑣ*=0k=0k=0k=03Ö×ᐹᨵqᦪØX஺8.ᔣÚX=5%2Û3'ᑣ|)1|+D+|2%3|Ü-ÝᔣÚᦪRGRRGß{+3%|+|à|ÜÝᔣÚᦪRGRRGáÃÄ⚪1.¯☢Ḅᦪä¿å•Âç⚗éᵨNewton3ïRðÂç⚗ḄᦪñsòðÂç⚗஺-2-10123-5111725p")2.ᵨᨬVáórsÂô᝞y=a+bx2Ḅö÷yøù¯ᑡᦪäúᔠ

5019253138441932.34973.397.8y11111CDi3.éïRᦪpx,᜛xypqý+iþÿḄ
ᑡ{x}▤ᦈᑮপ=0Ḅ᪷X*ok4.!ឋ#$%&y(eߟl,y“—by“+(+136+1,/“4&58H—17&8%9#▤Ḅ&5஻=-178%9▤Ḅ஺21Xi5.=8>?1312@ABᦪD▣ᑖGᡂIJᓫLMND▣OIJPNX21112210_%4D▣QR&ᓽ4=T஺ᯠVᵨXḄᑖGGY8>?஺1aa*06.Z[8>?4a1°%1@\]GY8>?ḄJacobibc%OGauss-seidelb஺“UI0c%ḄᦈḄᐙ⌕ᩩk஺7.=X*8>/1X,=0Ḅlm᪷஻?ு2,Newtonbc%uv!ឋᦈ&wᵨbcxyXk+\K./1X*,஺஺ᑣ{|ᑮ#▤}&\]஺

51DEὃB-GHI⚪/᪆஻=0,1,…&20>
1C,#include#includevoidmain()doubleIA[21],IB[21];inti;IA[0]=0.18232155,IB[20]=0.0087301587;//ᑭᵨ⌴xy(A),IAfor(i=l;i<=21;i++)(IA[i]=(-5.0)*IA[i-l]+1.0/i;)//ᑭᵨ⌴xy(B),IBfor(i=20;i>=1;i—)(IB[i-l]=-(IB[i]/5.0)+l/(5.0*i);)஻]printf("I⚪

52

53n\tI(A)\t\t\t\tn\tI(B)

54");for(i=0;i<21;i++){printf("%d\t%-18.10f\t\t%d\t%-18.10f

55",i,IA[i],i,IB[i]);:

56*D:\progra>\Debug\progra*l.exe*B-|q|x--⚪▲nInI00.182321550000.182321556810.088392250010.088392216020.058038750020.058038919830.043139583330.043138734140.034302083340.034306329650.028489583350.028468352260.024218750060.024324905570.021763392970.021232615280.016183035780.018836924290.030195932690.016926489910-0.0509796628100.0153675505110.3458074050110.014071338312-1.6457036916120.0129766419138.3054415350130.012039867614-41.4557791036140.011229233515207.3455621849150.010520499116-1036.6653109244160.0098975045175183.3853781514170.009336006718-25916.8713352015180.008875522119129584.4093075865190.008253968320-647921.9965379322200.0087301587|Pressanykeytocontinue.zJ#\ᦪ⊤012345-7-452665128/X.@ᵨLagrange%IJ⚗yᵫY/10.5,Ḅ஺>
(C)#include#includevoidmain()floatx[6]={0,1,2,3,4,5},y[6]={-7,-4,5,26,65,128),1[6]={1,1,1,14,1);floata=0.5,s=0.0;inti,j;for(i=0;iv=5;i++){for(j=0;j<=5;j++)(if(i!=j)(//²ᦪl[i]=l[i]*(a-xU])/(x[i]-x|j]);஻⚗ys+=HiJ*yliJ;,஻]

57printf("#⚪

58");printf(HTheresultis%6.3f

59'\s);:ᵨº»xyḄ⌴ᓄxyRᑖ⌕½¾¿ÀÁgxlO-5஺>
(C)#include#include஻ÃRᦪdoublefunc(doublex)(doublet;t=4.0/(l+x*x);returnt;voidmain()(inta=O,b=l,k=l,i,j;doubleT[lOOJ={O},s;஻º»xyḄ⌴ᓄxyT[0]=(b-a)*1.0/2.0*(func(a)+func(b));do{s=0;for(i=0;i0.000005);/Å]printf("⚪

60");for(j=0;j

61",pow(2,j),T|jJ)Æ)printf("ÇȽ¾⌕ḄRᑖ⊤|yḄ=%10.7f

62",TLk-lJ);:

63XH,⌕½¾¿ÀÁ1x10-5஺ÉᵨÊËÌ1RomberglÍxyRᑖ2>
(C)#include#includevoidmain()doubleT[4]={3.0,3.1,3.1311765,3.1389885},S[3],C[2],R;inti;஻Î⚪ÏᑮTḄprintf("É⚪

64");for(i=0;i<4;i++)printf("T[%.f]=%.7f

65",pow(2,i),T[i])Æfor(i=0;i<3;i++)S[i]=4.0*T[i+l]/3-T[i]/3.0;printf(,'S[%.f]=%.7f

66,,,pow(2,i),S[i]);for(i=0;i<2;i++)C[i]=16.0*S[i+l]/15-S[i]/15.0;printf(,,C[%.f]=%.7f

67,,,pow(2,i),C[i]);R=6410*C[l]/63-C[0]/63.0;"ÐÇȽ¾⌕ḄRᑖ⊤|yḄR=":

68=ÑÒ⚪.'XÓh=O.i,@ᵨEuler8%ஹV⌨ḄEuler8%I{0)=1Oº»xyG஺>
(C)#include#includevoidmain()(doubleX,Yl[6]={1.0},Y2[6]={1.0},Y3[6]={1.0},Y4[6]={1.0};inti;for(i=0;i<5;i++)(X=0.1*i;Yl[i+l]=0.9*Y1[i]+0.1*X+0.1;Y2[i+l]=(Y2[i]+0.1*X+0.11)/l.l;Y3[i+l]=(0.95*Y3[i]+0.1*X+0.105)/1.05;Y4[i]=X+exp(-1.0*X);)X=0.1*i;Y4[i]=X+exp(-1.0*X);஻]printf("⚪

69");printf("Xn\t\tEuler8%\tV⌨Euler8%\tº»xy\tÖ×G

70”)Æfor(i=0;i<6;i++)(printf(n%.lf\t%.6f\t%.6At%.6f\t%.6f

71H,0.1*i,Yl[i],Y2[i],Y3[i],Y4[i]);:

72\prograB\Debug\prograB5.exe*BEISI⚪▲Xn1iuleÙ8%V⌨Eulei*8%Ú»xyÖ×Gߟ0.01.0000001.0000001.0000001.0000000.11.0000001.0090911.0047621.00483?0.21.0100001.0264461.0185941.0187310.31.0290001.0513151.0406331.0408180.41.0561001.0830131.0700961.0703200.51.0904901.1209211.1062781.106531Pressanykeytocontinue#JÛᵨNewton%Mᑡ8>Ḅ᪷&Ö×ᑮÉLᨵᦔᦪÞ஺(1)/(1)=/I3ßI1=஺ᙠß0=2▬Ḅ᪷Æ(2)/(])=/I31I6*+2=0ᙠâ0=1▬Ḅ᪷஺>
(C)#include#includevoidmain()(inti=l,Nl,N2;doubleXl[100],X2[100];Xl[0]=X2[0]=2.0;஻ãᓫbcdo(Xl[i]=pow(3.0*X1,1.0/3.0);Nl=i;i++;}while(fabs(X1[i-1]-X1[i-2])>0.0005);஻äåbci=lÆdo(X2[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++Æ}while(fabs(X2[i-1]-X2[i-2])>0.0005);஻]printf("Û⚪

73“);printf("পãᓫbc%

74");for(i=0;i<=N1;i++)(printf(u%10.7f

75H,Xl[i]);printf("ᑭᵨãᓫbc%ÇÈᨵᦔᦪÞḄ8>Ḅ᪷x=%6.3f

76H,Xl[Nl-l]);primf("পNewton%

77”)Æfor(i=0;i<=N2;i++)

78printf("%10.7f

79",X2[i]);}printf("ᑭᵨäå%ÇÈᨵᦔᦪÞḄ8>Ḅ᪷x=%6.3f

80",X2[N2-l]);)<-0.00222Yr,1f0.4)æ.\!ឋ8>?]on-Iᑘ6Z[è×G:nU.7/olI9ZSjU1,=1.JoIO5056254TJ17.4178,ஹ3.996x*=(1.92730,-0.698496,0.900432)&(1)ᵨéêëì%GY!ឋ8>?Æ(2)ᵨᑡíᐗïëì%G!ឋ8>?஺>
(MATLAB>
)clear;clc;D=zeros(3,4)ÆE=zeros(3,4)ÆA=[-0.00222;10.781250;3.9965.56254];B=l0.41.38167.4178;C=[ABJD(1,:)=C(1,:);E(1,:)=C(1,:);fori=2:3forj=1:4D(ij)=C(i,j)+C(l,j)*(-l)*C(i,l)/C(l,l)endendE(2,:)=D(2,:);forj=2:4E(3,j)=D(3,j)+D(2,j)*(-l)*D(3,2)/D(2,2);end

81B1=E(:,4);x3=vpa(Bl(3)/E(3,3),8);x2=vpa((B1(2)-E(2,3)*x3)/E(2,2),8);xl=vpa((B1(1)-E(1,3)*x3-E(1,2)*x2)/E(1,1),8);x=[xlx2x3]ᵨᑡíᐗïëì%G!ឋ8>?GḄ8>Ḅ᪷v:x=[1.9273000,-.69849600,.90042330]<430ஹ24öᵨSORbc%G8>?34-130஺8>?ḄÖ×GvX*=3,4,-5ஹX21°-14-24J>
(C)#include#includevoidmain()doublex1[6]={1.0},x2[6]={1.0},x3[6]={1.0};doublew[2]={1.0,1.25};inti,j;printf("ö⚪

82")for(i=0;i<2;i++)printf("bcᦪkw=%f

83n,w[i]);printf("\txI(k)\t\tx2(k)\t\tx3(k)

84n);for(j=lj<6;j++)x1[j]=x1[j-1]+w[i]*(244*x1[j-1]-3*x2[j1])/4.0;x2fj]=x2[j-l]+w[i]*(30-3*xl|jl-4*x2[j-l]+x3[j-ll)/4.0;x3[j]=x3[j-l]+w[i]*(-24+x2|j]-4*x3[j-l])/4.0;printf(u%d\t%.7f\t%.7f\t%.7^n"j,xl[jLx2[jLx3[j]);:

85c)*D:\progra*\Debug\progra>8.exe*-÷Xö⚪▲bcᦪkw=l.000000xlx2x315.25000003.8125000-5.046875023.14062503.8828125-5.029296933.08789063.9267578-5.018310543.05493163.9542236-5.011444153.03433233.9713898-5.0071526bcᦪk“=1.250000xlx2x316.31250003.5195313-6.650146522.62231453.9585266-4.600423833.13330274.0102646-5.096686342.95705124.0074838-4.973489?53.00372114.0029250-5.0057135Pressanykeytocontinue