数值分析实验答案.doc

实验0 截断误差与舍入误差#include stdio.h#include math.hconst double ln2=0.693147190546;const double e1=5e-6;void main() int sign; double s; long i; s=0.0; sign=1; i=1; while(fabs(ln2-s)=e1) s+=(1.0/i)*sign; sign=-sign; i+; printf(n=%ldn,i-1); getch();实验1 拉格朗日插值法编写拉格朗日插值法通用子程序，并用以下函数表来上机求,。x0.00.10.1950.30.4010.5f (x)0.398940.396950.391420.381380.368120.35206#include main() static float Lx10,Ly10; int n,i,j; float x,y,p; printf(enter n=); scanf(%d,&n); printf(enter xin); for(i=0;in;i+) scanf(%f,&Lxi); printf(enter yin); for(i=0;in;i+) scanf(%f,&Lyi); printf(enter x=); scanf(%f,&x); /* n=6; Lx0=0; Lx1=0.1; Lx2=0.195; Lx3=0.3; Lx4=0.401; Lx5=0.5; Ly0=0.39894; Ly1=0.39695; Ly2=0.39142; Ly3=0.38138; Ly4=0.36812; Ly5=0.35206; x=0.15; */ for( i=0;in;i+) p=1; for(j=0;jn;j+) if(i!=j) p=p*(x-Lxj)/(Lxi-Lxj); y+=p*Lyi; printf(y=%fn,y); getch();实验2 最小二乘法测得铜导线在温度()时的电阻如下表，求电阻R与温度T的近似函数关系。i0123456()19.125.030.136.040.045.150.076.3077.8079.2580.8082.3583.9085.10#include #include float gs(float a2020,float b20,int n )int i,j,k,l; float s; k=1;while(k!=n+1)if(akk!=0)for(i=k+1;i=n+1;i+)aik=aik/akk;bi=bi-aik*bk;for(j=k+1;j=1;k-)s=0;for(l=k+1;l=n+1;l+)s=s+akl*bl;bk=(bk-s)/akk; return 0;main()static float b20,Lx20,Ly20,c2020,ct2020,a2020;int m,n,i,j,k=0,l;float s,rtn;printf(enter m=);scanf(%d,&m); printf(enter n=); scanf(%d,&n);printf(enter xin); for(i=1;i=m;i+) scanf(%f,&Lxi);printf(enter yin); for(i=1;i=m;i+) scanf(%f,&Lyi);for( i=1;i=m;i+) ci1=1; for(j=2;j=n+1;j+) cij=Lxi*cij-1; for( i=1;i=m;i+) for(j=1;j=n+1;j+) ctji=cij; for( i=1;i=n+1;i+) for(j=1;j=n+1;j+) aij=0; for( i=1;i=n+1;i+) bi=0; for( i=1;i=n+1;i+) for(k=1;k=n+1;k+) for(j=1;j=m;j+)aik=aik+ctij*cjk; for(i=1;i=n+1;i+) for(j=1;j=m;j+) bi+=ctij*Lyj;gs(a,b,n);printf(nThe result is:);for(i=1;i=n+1;i+) j=i-1; printf(na%d=%f,j,bi); 实验3 变步长复合梯形公式求 的近似值。（1）编写定步长复合梯形程序求解上式；（2）编写变步长复合梯形程序求解上式，使误差不超过10-6。#includemath.hdouble f(double x) double f1; f1=4/(1+x*x);return(f1) ;double trapezia2(int k,double h,double a,double tn) double t2n,s=0; int i; t2n=tn/2; for(i=1;i=pow(2,k);i+) s+=f(a+(2*i-1)*h); t2n=t2n+s*h; return t2n; void main()double a,b,h,Tn,T2n,e; int n,k; printf(please input a,b,n,en); scanf(%lf%lf%d%lf,&a,&b,&n,&e); h=b-a; Tn=(b-a)*(f(a)+f(b)/2; for(k=0;kn;k+) h=h/2; T2n=trapezia2(k,h,a,Tn); if(fabs(T2n-Tn)e) break; printf(%lfn,Tn); Tn=T2n; printf(%lfn,Tn);实验3 定步长复合梯形公式double f(double x) return(4/(1+x*x) ;float trapezia(int n,float h,float a)float fk=0; int i; for(i=1;in;i+) fk+=f(a+i*h); return(fk*h);void main()float a,b,h,Tn; int n; printf(please input a,b,n); scanf(%f%f%d,&a,&b,&n); h=(b-a)/n; Tn=(f(a)+f(b)*h/2; Tn+=trapezia(n,h,a); printf(%f,Tn) ;实验5 非线性方程求解编写Newton迭代法通用子程序。实现方程f(x)=x6-x-1=0的满足精度要求的解。要求求解过程中用一个变量I控制三种状态，其中：i=0表示求解满足给定精度的近似解；i=1表示f(x0)=0，计算中断；i=2表示迭代n次后精度要求仍不满足。#define N 1000#includemain() double x,x0,p=1e-6; double f(double x),g(double x); int i,j,k,n=0; printf(n enter x0:); scanf(%lf,&x0); do x=x0-f(x0)/g(x0); printf(n %d %12.8lf %8.3le,n,x0,f(x0); if(np); printf(n the result is:%lf,x0);/*MAIN*/double f(double x) return(pow(x,6)-x-1);/*F(X)*/double g(double x) return(6*pow(x,5)-1);/*G(X)*/实验6 高斯消元法编写选列主元的高斯消去法。求出下列线性方程组Ax=b的解x。#include #define N 10main()int i,ik,k=0,j,l,n,max;static float aNN,bN,t,s,min=1e-6;printf(n enter n:);scanf(%d,&n);printf(nenter A=(aij)(line first):);for(i=0;in;i+)for(j=0;jn;j+)scanf(%f,&aij);printf(nenter b:);for(i=0;in;i+)scanf(%f,&bi);for(k=0;kn-1;k+) max=0; for(i=k;in;i+) if (max-fabs(aik)0) max=fabs(aik); ik=i; if(maxmin) break;if(ik!=k)for(j=k;jn;j+) t=aikj;aikj=akj;akj=t;t=bik;bik=bk;bk=t;for(i=k+1;in;i+) aik=aik/akk; for(j=k+1;j=0;i-) for(j=i+1;jn;j+) bi= bi- aij* bj; bi= bi/aii; printf(nThe result is:);for(i=0;in;i+)j=n-i;printf(nx%d=%f,j,bi);实验7 改进欧拉法#include math.h#include stdio.hfloat f(float x, float y) return(2.0/x*y+x*x*exp(x); float g(float x) return(x*x*(exp(x)-exp(1); void main()float x,y,h,a,b,a0,yp,yc; printf(please input a,b,h and a0n); scanf(%f%f%f%f,&a,&b,&h,&a0); x=a; y=a0; while(x=b+h) printf(x=%f,y=%f,y(x)=%f,y(x)-y=%fn,x,y,g(x),fabs(y-g(x); yp=y+h*f(x,y); x+=h; yc=y+h*f(x,yp); y=0.5*(yp+yc); 实验7 龙格库塔法#include #define f(x,y) (x-y)main()float a,b,h,x,y,k1,k2,k3,k4,y0,x0;int n=0,i,j,N;clrscr();printf(n enter N:);scanf(%d,&N);printf(nenter a,b:);scanf(%f%f,&a,&b);printf(n enter primary data y(0): );sca