數(shù)值分析五個題目的C語言及Matlab程序

1、本文檔包含上一個文檔中的五個數(shù)值分析實驗題C語言程序及Matlab程序?qū)嶒炓籆程序#include stdio.h#include math.hvoid main()int i=0;float a=0.1,b=1.9,t=0.0,e=1.9;if(pow(a,7)-28*pow(a,4)+14)*(pow(b,7)-28*pow(b,4)+14)0)if(7*pow(x,6)-112*pow(x,3)printf(x=%f,i=%d,e=%fn,x,i,e);for(i=1;i0.00001;i+)t=x;x=x-(pow(x,7)-28*pow(x,4)+14)/(7*pow(x,6)-11

2、2*pow(x,3);e=fabs(t-x);printf(x=%f,i=%d,e=%fn,x,i,e);Matable 程序i=0;x=1.9;t=0.0;e=1.9;disp(i=,num2str(i), ,x=,num2str(x), ,e=,num2str(e);for i=1:7 t=x; x=x-(x7-28*x4+14)/(7*x6-112*x3); e=abs(t-x); disp(i=,num2str(i), ,x=,num2str(x), ,e=,num2str(e); if e0.00001 break; endend實驗二C程序#includestdio.h#inclu

3、demath.h/已知量double x10=1,2,3,4,5,6,7,8,9,10;double fd1=1,fd2=0.1;double fx10=0,0.69314718,1.0986123,1.3862944,1.6094378, 1.7917595,1.9459101,2.079445,2.1972246,2.3025851; /函數(shù)聲明void canshu(double *h,double *r,double *u,double *d);void wanju(double *u,double *r,double *d,double *m);double yths(double

4、*m,double *h,double p);double ytdhs(double *m,double *h,double p);/主函數(shù)void main()double p,q1,q2;double h9,u9,r9,m10,d10;/ 矩陣Am=d參數(shù)數(shù)據(jù)u8=1,r0=1;canshu(h,r,u,d);wanju(u,r,d,m);printf(請輸入待求數(shù)值：x=);scanf(%lf,&p);q1=yths(m,h,p);q2=ytdhs(m,h,p);printf(輸出結(jié)果為:nf(%lf)=%lfnf(%lf)=%lfn,p,q1,p,q2);/求參函數(shù)void cansh

5、u(double *h,double *r,double *u,double *d)int i,j;double a10;for(i=0;i-1)ri=hj+1/(hj+1+hj);uj=hj/(hj+hj+1);di=(6/(hj+hi)*(ai-aj);d0=(6/h0)*(ai-9-fd1);d9=(6/hi-1)*(fd2-ai-1);/追趕法求彎矩向量mvoid wanju(double *u,double *r,double *d,double *m)int i,j;double l9,n10,z10;n0=2;z0=d0;for(i=0;i-1;j-)mj=(zj-rj*mj+1

6、)/nj;/三次樣條插值函數(shù)double yths(double *m,double *h,double p)int i,j=0;double q;for(i=0;i10;i+)if(xi=(p-1)break;q=pow(xi+1-p,3)/6/hi+1*mi+pow(p-xi,3)/6/hi+1*mi+1+ (fxi-pow(hi+1,2)*mi/6)*(xi+1-p)/hi+1+ (fxi+1-pow(hi+1,2)*mi+1/6)*(p-xi)/hi+1;return q;/三次樣條插值導(dǎo)函數(shù)double ytdhs(double *m,double *h,double p)int i

7、,j=0;double q;for(i=0;i10;i+)if(xi=(p-1)break;q=-pow(xi+1-p,2)/2/hi+1*mi+pow(p-xi,2)/2/hi+1*mi+1-(fxi-pow(hi+1,2)*mi/6)/hi+1+(fxi+1-pow(hi+1,2)*mi+1/6)/hi+1;return q;Matlab 程序functionh,r,u,d=canshu(x,fx,h,r,u,d,fd1,fd2)%UNTITLED10 Summary of this function goes here% Detailed explanation goes herefor

8、 i=1:9 h(i)=x(i+1)-x(i); a(i)=(fx(i)-fx(i+1)/(x(i)-x(i+1); j=i-1; if j0 r(i)=h(j+1)/(h(j+1)+h(j); u(j)=h(j)/(h(j)+h(j+1); d(i)=(6/(h(j)+h(i)*(a(i)-a(j); end endd(1)=(6/h(1)*(a(i-8)-fd1);d(10)=(6/h(i)*(fd2-a(i);endglobal x fd1 fd2 fx h d m r u;x=1,2,3,4,5,6,7,8,9,10;fd1=1;fd2=0.1;fx=0,0.69314718,1.09

9、86123,1.3862944,1.6094378,1.7917595,1.9459101,2.079445,2.1972246,2.3025851;u(9)=1;r(1)=1;h,r,u,d=canshu(x,fx,h,r,u,d,fd1,fd2);m=wanju(u,r,d,m);p=input(請輸入待求數(shù)值:x=);q1=yths(m,h,p,x,fx);q2=ytdhs(m,h,p,fx,x);disp(輸出結(jié)果為:,f(,num2str(p),)=,num2str(q1),f(,num2str(p),)=,num2str(q2);functionm=wanju(u,r,d,m)%U

10、NTITLED12 Summary of this function goes here% Detailed explanation goes heren(1)=2;z(1)=d(1);for i=1:9 l(i)=u(i)/n(i); n(i+1)=2-l(i)*r(i); z(i+1)=d(i+1)-l(i)*z(i); endm(10)=z(10)/n(10);for j=9:-1:1 m(j)=(z(j)-r(j)*m(j+1)/n(j);endendfunction q =ytdhs(m,h,p,fx,x)%UNTITLED14 Summary of this function go

11、es here% Detailed explanation goes herefor i=1:10 if x(i)=(p) break; endq=-(x(i+1)-p)2/2/h(i+1)*m(i)+(p-x(i)2/2/h(i+1)*m(i+1)-(fx(i)-(h(i+1)2*m(i)/6)/h(i+1)+(fx(i+1)-(h(i+1)2*m(i+1)/6)/h(i+1);endendfunctionq=yths(m,h,p,x,fx)%UNTITLED13 Summary of this function goes here% Detailed explanation goes he

12、refor i=1:10if x(i)=(p)break;endq=(x(i+1)-p)3/6/h(i+1)*m(i)+(p-x(i)3/6/h(i+1)*m(i+1)+(fx(i)-(h(i+1)2*m(i)/6)*(x(i+1)-p)/h(i+1)+(fx(i+1)-(h(i+1)2*m(i+1)/6)*(p-x(i)/h(i+1);endend實驗三C程序#includestdio.h#includemath.h/已知量double b=3,a=1;/函數(shù)聲明double romberg();double fhs(double x);/主函數(shù)void main()double q;q=r

13、omberg();printf(輸出結(jié)果為：r=%lfn,q);/Romberg算法double romberg()int n,j,k=0,m=0,z=0,i;double e=1,qh=0,q,h,x0,r1=0,t50,s50,c50,r50;t0=(b-a)/2*(fhs(a)+fhs(b);for(i=1;1;i+)n=pow(2,i-1);h=(b-a)/n;x0=a+0.5*h;for(j=0;j=3)for(k;ki;k+)sk=(4*tk+1-tk)/3;for(m;mk-1;m+)cm=(16*sm+1-sm)/15;for(z;zm-1;z+)rz=(64*cz+1-cz)

14、/63;e=fabs(r1-rz-1);r1=rz-1;if(e=4 for k=k:i s(k)=(4*t(k+1)-t(k)/3; end for m=m:k-1 c(m)=(16*s(m+1)-s(m)/15; end for z=z:m-1 r(z)=(64*c(z+1)-c(z)/63; end e=abs(r1-r(z-1); r1=r(z-1); end if(e0.00001) break; endendq=r(z-1);endglobal b a k m z e qh r1;k=0;m=0;z=0;e=1;qh=0;r1=0;b=3;a=1;q=romberg();disp(

15、輸出結(jié)果為：r=,num2str(q);實驗四C程序#includestdio.h#includemath.h/已知量double x=0,h=0.0005,y3=0,p4=0.025,0.045,0.085,0.1;double fx(double x,double y3,int t);void main()int i,t;double k4,m3;for(i=0;i4;i+)for(x=0;x=pi;x=x+h)for(t=0;t3;t+)mt=yt;for(t=0;t3;t+)k0=fx(x,m,t);mt=yt+0.5*h*k0;k1=fx(x+0.5*h,m,t);mt=yt+0.5

16、*h*k1;k2=fx(x+0.5*h,m,t);mt=yt+h*k2;k3=fx(x+h,m,t);/mt=yt;yt=yt+h*(k0+2*k1+2*k2+k3)/6;x=0;for(t=0;t3;t+)printf(y%d(%lf)=%lft,t+1,pi,yt);printf(n);for(t=0;t3;t+)yt=0;double fx(double x,double y3,int t)double f;if(t=0)f=0*x+1;else if(t=1)f=0*x+y2;elsef=0*x+1000-1000*y1-100*y2;return f;Matlab 程序functio

17、nf=fx(x,y)%UNTITLED7 Summary of this function goes here% Detailed explanation goes heref(1)=0*x+1;f(2)=0*x+y(3);f(3)=0*x+1000-1000*y(2)-100*y(3);endy=zeros(1,3);h=0.0005;x=0;p=0.025,0.045,0.085,0.1;k=zeros(4,3);for i=1:4 for j=1:fix(p(i)/h) k(1,:)=fx(x,y); k(2,:)=fx(x+0.5*h,y+0.5*h*k(1,:); k(3,:)=fx

18、(x+0.5*h,y+0.5*h*k(2,:); k(4,:)=fx(x+h,y+h*k(3,:); y=y+h*(k(1,:)+2*k(2,:)+2*k(3,:)+k(4,:)/6; x=x+h; end disp(x=,num2str(p(i), ,y=,num2str(y); y=zeros(1,3);end實驗五C程序#includestdio.h#includemath.h#define N 9/已知量double ANN=12.38412,2.115237,-1.061074,1.112336,-0.113584,0.718719,1.742382,3.067813,-2.0317

19、43,2.115237,19.141823,-3.125432,-1.012345,2.189736,1.563849,-0.784165,1.112348,3.123124,-1.061074,-3.125432,15.567914,3.123848,2.031454,1.836742,-1.056781,0.336993,-1.010103,1.112336,-1.012345,3.123848,27.108437,4.101011,-3.741856,2.101023,-0.71828,-0.037585,-0.113584,2.189736,2.031454,4.101011,19.8

20、97918,0.431637,-3.111223,2.121314,1.784317, 0.718719,1.563849,1.836742,-3.741856,0.431637,9.789356,-0.103458,-1.103456,0.238417, 1.742382,-0.784165,-1.056781,2.101023,-3.111223,-0.103458,14.7138465,3.123789,-2.213474, 3.067813,1.112348,0.336993,-0.71828,2.121314,-1.103456, 3.123789,30.719334,4.44678

21、2, -2.031743,3.123124,-1.010103,-0.037585,1.784317,0.238417,-2.213474,4.446782,40.00001;double b9=2.1874369,33.992318,-25.173417,-0.84671695,1.784317,-86.612343,1.1101230,4.719345,-5.6784392;/函數(shù)聲明void change(int a,int b);/主函數(shù)void main()int i,j,q1,n,m,t;double tmp1,tmp2=0,x9,tmp3;for(i=0;i9;i+)tmp1=A

22、ii;q1=i;for(j=i;j9;j+)/if(fabs(tmp1)fabs(Aji)tmp1=Aji;q1=j;if(q1!=i)change(i,q1);for(n=i+1;n9;n+)tmp3=Aii/Ani;for(m=i+1;m=0;t-)int l,p;l=8-t;for(p=1;p=l;p+)tmp2+=Att+p*xt+p/Att;xt=bt/Att-tmp2;tmp2=0;printf(x%d=%lfn,t,xt);/交換對應(yīng)行void change(int a,int d)int i;double tmp;tmp=ba;ba=bd;bd=tmp;for(i=0;i9;i

23、+)tmp=Aai;Aai=Adi;Adi=tmp;Matlab程序A=12.38412,2.115237,-1.061074,1.112336,-0.113584,0.718719,1.742382,3.067813,-2.031743;2.115237,19.141823,-3.125432,-1.012345,2.189736,1.563849,-0.784165,1.112348,3.123124;-1.061074,-3.125432,15.567914,3.123848,2.031454,1.836742,-1.056781,0.336993,-1.010103;1.112336,-1.012345,3.123848,27.108437,4.101011,-3.741856,2.101023,-0.71828,-0.037585;-0.113584,2.189736,2.031454,4.101011,19.897918,0.431637,-3.111223,2.121314,1.784317; 0.718719,1.563849,1.836742,-3.741856,0.431637,9.789356,-0.103458,-1.103456,0.238417; 1.742382,-0.784165,-1.05678