数值计算方法上机答案.docx

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1、数值计算方法上机答案一、求非线性方程的根。1、求方程()cos0fxxx=-=在01.5x=附近的是根，要求精度知足3110kkxx-+-结果：0.7390852、求方程32()0.80fxxx=-=在01x=附近的是根，求出具有思维有效数字的根近似值.(简单迭代法)clearclcphi=inline(0.8+x2)(1/3);%迭代函数x0=input(x0=);del=input(del=);N=input(N=);n=1;fprintf(n%2d%f,0,x0);whilen二、求解线性方程组直接法或迭代法1、?-=?-=?-22118118344108318311231224321x

2、xxxx(列主元素消元法)a=input(a=)%2,2,1,-3,8;-2,1,-1,-3,1;8,-1,3,8,-1;10,4,4,3,8;p,n=size(a);forw=1:px,y=find(a(w:p,w)=max(max(a(w:p,w);q=a(w,:);a(w,:)=a(x,:);a(x,:)=q;endforj=1:(p-1)fori=(j+1):pa(i,:)=a(j,j)/a(i,j).*a(i,:)-a(j,:);endendm=p;whilem1s(m)=a(m,n);j=p;while(j2)&(j=m+1)&(jx=1.0000-1.00002.0000-2.0

3、000。误差限准确解、)(61,654321818.117304.29236.24054322.2223.0803.2155.43211.0918.491.0017.0812.0101.0999.817.12705.61907.311.3501.45.115.0135.007.13.61.21211.3410006.1007.1991.2615.0031.17,2-=?-=?-=?-=EExbAbAxfunctionx,det,flag=Gauss(A,b)n,m=size(A);nb=length(b);ifn=merror(therowsandcloumsofAmustbeequal!);

4、return;endifm=nberror(therowsandcloumsofAmustbeequalthelengthofb!);return;endflag=OK;det=1;x=zeros(n,1);fork=1:(n-1)max1=0;fori=k:nifabs(A(i,k)max1max1=abs(A(i,k);r=i;endendifmax1kforj=k:nz=A(k,j);A(k,j)=A(r,j);A(r,j)=z;endz=b(k);b(k)=b(r);b(r)=z;det=-det;endfori=k+1:nm=A(i,k)/A(k,k);forj=k+1:nA(i,j

5、)=A(i,j)-m*A(k,j);endb(i)=b(i)-m*b(k);enddet=det*A(k,k);enddet=det*A(n,n);ifabs(A(n,n)-1.0,34.211,-1.0,-2.1,6.3,-1.70,0.5,13.0,-0.5,1.0,-1.54.501,3.11,-3.907,-61.705,12.17,8.9990.101,-0.812,-0.017,-0.91,4.918,0.11.0,2.0,3.0,4.5,5.0,21.8Gauss(A,b)A=17.031,-0.615,-2.991,1.007,-1.006,0-1.0,34.211,-1.0,

6、-2.1,6.3,-1.70,0.5,13.0,-0.5,1.0,-1.54.501,3.11,-3.907,-61.705,12.17,8.9990.101,-0.812,-0.017,-0.91,4.918,0.11.0,2.0,3.0,4.5,5.0,21.8ans=1.0000-2.00002.9999-4.00015.0000-6.0008()418823.40443.77424.24767.87589.70308.24955.0,1992.421735261371143711071111152198215438112217124211571311431111421125281141

7、12711027321341173-=-=?-=?-=EExbAT其中准确解、clearclcn=input(n=);A=input(A=);b=input(b=);x=input(x=);epsilon=input(n精度=);N=input(n最大迭代次数N=);fprintf(n%d:,0);fori=1:nfprintf(%f,x(i);end%下面是迭代经过fork=1:N%这是第k步迭代，迭代前的向量在x0中，迭代后的向量在x中；normal=0;fori=1:nt=x(i);x(i)=b(i);forj=1:nifj=ix(i)=x(i)-A(i,j)*x(j);endendx(

8、i)=x(i)/A(i,i);temp=abs(x(i)-t);%求范数于迭代在同一个循环中；iftempnormalnormal=temp;%这里用的是无穷范数endend%第i不迭代结束；fprintf(n%d:,k);fori=1:nfprintf(%f,x(i);%输出迭代经过endifnormal最大迭代次数N=1000:0.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000001:4.1764714.3000001.3750003.3636364.0666674.3333333.8421052.1000002:2

9、.9225162.0834500.5552548.5693667.2030702.3916968.4193711.7707083:1.796703-1.159744-1.3226198.9108208.2232983.3576457.2909535.8926324:4.2118430.507676-1.2417916.9272028.8477911.5521346.9022046.1490355:4.8681201.868149-2.5922027.3796888.4218241.2958416.8839584.9358786:4.5347650.742110-2.3382647.865994

10、8.5206412.9955406.6619884.5317467:4.1340460.204098-1.9753807.8475618.5522223.1606677.1482374.4215358:3.9348030.230528-2.0501637.8467958.3502823.0342277.1274764.9682709:4.1827670.456461-1.8566067.7032878.4770762.7098147.0649175.05072110:4.2398730.623716-2.0374607.7409308.4934282.5261337.0804484.90047

11、111:4.2239090.527844-2.0911437.7663918.4818132.7290846.9876304.90038812:4.2294720.494477-2.0251787.7442958.4957602.7621067.0363614.83435113:4.1809570.483627-2.0503767.7731678.4616392.7712547.0548314.86272214:4.1877690.472362-2.0135997.7616418.4737412.7694887.0430224.89630015:4.1986420.499955-2.02107

12、27.7553988.4794262.7237627.0548634.88461616:4.1986920.501255-2.0384687.7601448.4745152.7349437.0402094.89122117:4.2055730.498191-2.0286037.7557178.4802942.7405807.0410484.88046418:4.1993120.497105-2.0346057.7600978.4761272.7421377.0457024.87738819:4.1974990.492006-2.0308367.7600368.4757992.7481837.0

13、430294.88347420:4.1991700.494820-2.0284517.7582898.4772642.7418767.0458104.88202121:4.1984870.496008-2.0317677.7593908.4761002.7413467.0445474.88355522:4.1998550.495605-2.0303137.7585468.4771302.7422207.0436914.88305223:4.1995870.496071-2.0311267.7588478.4768822.7416557.0445844.88176324:4.1990620.49

14、5235-2.0312187.7591598.4765432.7430467.0440424.88255825:4.1993170.495278-2.0304527.7588308.4768572.7425887.0444094.88233026:4.1991060.495514-2.0309467.7590208.4766402.7422837.0444594.88248927:4.1992540.495419-2.0307707.7589248.4767442.7424677.0442214.88264528:4.1993260.495564-2.0307947.7588918.47678

15、82.7422487.0443704.88239829:4.1992300.495486-2.0309247.7589758.4767042.7424297.0442904.88248430:4.1992730.495441-2.0307827.7589238.4767582.7424537.0443054.88246231:4.1992410.495482-2.0308407.7589468.4767312.7423837.0443504.882449xx=4.19920.4955-2.03087.75898.47677.04444.8824.61,)1,5,10,10,5(00001)(7

16、035155135202041151063154321111114-=-=?=?=EExbpascalAT准确解矩阵、functionx,det,flag=Gauss(A,b)n,m=size(A);nb=length(b);ifn=merror(therowsandcloumsofAmustbeequal!);return;endifm=nberror(therowsandcloumsofAmustbeequalthelengthofb!);return;endflag=OK;det=1;x=zeros(n,1);fork=1:(n-1)max1=0;fori=k:nifabs(A(i,k)max1max1=abs(A(i,k);r=i;endendifmax1kforj=k:nz=A(k,j);A(k,j)=A(r,j);A(r,j)=z;endz=b(k);b(k)=b(r);b(r)=z;det=-det;endfori=k+1:nm=A(i,k)/A(k,k);forj=k+1:nA(i,j)=A(i,j)-m*A(k,j);b(i)=b(i)-m*b(k);enddet=det*A(k,k);enddet=det*A(n,n);ifabs(A(n,n)Gauss(A,b)ans=5-1010-51三、用追赶法求解下列方程组6位有效数字。