计算方法程序

1、一、对分法1、#include"math.h"main() float a3=-3.0,1.0,0.0,b3=-2,0,1,c3;float f(float x);int i;for(i=0;i<3;i+)do ci=(ai+bi)/2.0; if(f(ci)=0) exit(0);else if(f(ci)*f(ai)<0) bi=ci; else ai=ci; while(bi-ai)>1e-5); ci=ai; printf("the roots are:"); for(i=0;i<3;i+)printf("%f&

2、quot;,ci);printf("2.000000");float f(float x)float y;y=x*x*x-2*x*x-4*x-7;return(y);3、对分部分函数调用（题目要求如2）#include "math.h"float f(float x) float y; y=x*x*x-2*x*x-4*x-7; return(y); float f1(float a ,float b) float c; do c=(a+b)/2; if(f(c)=0) exit(0); else if(f(a)*f(c)<0) b=c; else

3、a=c; while(b-a)>1e-5); return(a); main() float a=3.0,b=4.0,s; s=f1(a,b); printf("the root is %f",s);2、用对分法求出方程x-2x-4x-7=0在区间【3，4】内的根，精度要求为10。#include"math.h"main()float a=3.0,b=4.0,c;float f(float x);do c=(a+b)/2.0; if(f(c)=0)printf("the root is %f",c); exit(0);/*找到方

4、程的根*/ else if(f(c)*f(a)<0) b=c; else a=c; while(b-a)>1e-5);printf("the root is %f",a);float f(float x)float y;y=x*x*x-2*x*x-4*x-7;return(y);对分法的算法：扫描法的算法：4、对分法和扫描结合求方程x-5x+x+2=0的实根的上、下界，实现根的隔离，并用对分法求出所有的实根，精度要求为10。此方程的4个实根分别为：root=2.246979 root=0.554956 root=0.801941 root=2.000000#in

5、clude "math.h"float f(float x) float y;y=x*x*x*x-5*x*x+x+2;return y;main()float a,b,c;int i=0;float x,h=0.001,p5,q5,n;scanf("%f%f",&a,&b) ;x=a; while(x<b) if(f(x)*f(x+h)<=0) pi=x;qi=x+h;i=i+1;printf("%f,%fn", pi, qi); x=x+h; n=i; for(i=0;i<n;i+) a=pi;b=

6、qi; while(b-a>1e-5) c=(a+b)/2; if(f(c)=0) printf("%fn",c);exit(0); else if(f(a)*f(c)<0) b=c; else a=c; printf("%fn",c) ; 二、秦九韶算法使用秦九韶算法计算多项式的值ax+ax+ax+a 例如计算3x+2x+1,当x=-1时值为2。main()float aa20,y,x; int i,n;printf("input duo xiang shi ci shu n:n" ) ;scanf("%d&q

7、uot;,&n);printf("input duo xiang shi de xi shun");for(i=0;i<=n;i+) scanf("%f",&aai);printf("input xn");scanf("%f",&x);y=aa0;for(i=1;i<=n;i+) y=y*x+aai;printf("pn=%fn",y);秦九韶算法：三、牛顿法1、编写牛顿法求方程根的通用程序，精度要求为10。（x-x-2x-3=0 初值 x=2）#includ

8、e"math.h"main()float f(float x);float fd(float x);float x,x0,x1;x1=2.0;do x0=x1; x1=x0-f(x0)/fd(x0); while(fabs(x1-x0)>1e-5);printf("the root is%fn",x1);float f(float x)return x*x*x-x*x-2*x-3;float fd(float x)return 3*x*x-2*x-2;2、用牛顿法求a的立方根，精度要求为0.000005。#include"math.h&q

9、uot;main()double x0,x1;int a;printf("input an");scanf("%d",&a);if(a=0)printf("a=0n");exit(0);x1=a;do x0=x1; x1=x0-(x*x*x-a)/(3*x*x); while(fabs(x1-x0)>=0.5e-5);printf("the root is%fn",x1);printf("root=%fn",x1);3、用牛顿法求方程x-e=0（x-exp(-x)=0）在1附近的根

10、，精度要求为0.00001。#include"math.h"main()float x0,x1;x1=1.0;do x0=x1;x1=x0-(x-exp(-x)/(1+exp(-x);while(fabs(x1-x0)>1e-5);printf("the root is%fn",x1);牛顿法的算法：四、列主元高斯消元法(通用程序)#include"math.h"#define M 3#define N 3main()float aMN+1,xN,temp,l,s;int i,j,k,r;printf("please

11、input the date:n");for(i=0;i<M;i+) for(j=0;j<N+1;j+) scanf("%f",&aij);for(k=0;k<N-1;k+) r=k; for(i=k+1;i<=M-1;i+) if(fabs(aik)>fabs(ark) r=i; if(ark=0) printf("QYn"); exit(0); else if(r!=k) for(j=k;j<=N;j+) temp=akj; akj=arj; arj=temp; for(i=k+1;i<=N

12、-1;i+) l=aik/akk;for(j=k+1;j<=N;j+) aij=aij-l*akj; for(k=N-1;k>=0;k-) s =0.0; for(j=k+1;j<=N-1;j+) s = s +akj*xj; xk=(akN- s)/akk; for(i=0;i<=N-1;i+)printf("x%d=%fn",i,xi); 列主元高斯消元法的算法：五、LU分解法用LU分解法解线性方程组，系数矩阵由二维数组a给出，右端由b数组给出。#include"math.h"main()int i,j,k,m,n=4;flo

13、at t;float b4=1,1,-1,-1;float a44=4,3,2,1,3,4,3,2,2,3,4,3,1,2,3,4;for(k=0;k<n;k+) for(j=k;j<n;j+) t=0; for(m=0;m<=k-1;m+) t=t+akm*amj; akj=akj-t; for(i=k+1;i<n;i+) t=0; for(m=0;m<=k-1;m+) t=t+aim*amk; aik=(aik-t)/akk; for(i=0;i<n;i+) t=0; for(j=0;j<=i-1;j+) t=t+aij*bj; bi=bi-t;

14、for(i=n-1;i>=0;i-) t=0; for(k=i+1;k<n;k+) t=t+aik*bk; bi=(bi-t)/aii; for(i=0;i<n;i+) printf("%10.4f",bi);LU分解法的算法：六、雅可比迭代法1、通用程序#define N 4#include"math.h"float cha(x,y)float xN,yN;float z;int i,k;z=fabs(y0-x0);for(i=1;i<N;i+)if(fabs(yi-xi)>z) z=fabs(yi-xi);return

15、(z);main()float aNN,bN,xN,yN,h;int i,j,k;float t=0,s;for(i=0;i<N;i+) for(j=0;j<N;j+) scanf("%f",&h); aij=h; for(i=0;i<N;i+) scanf("%f",&h); bi=h;yi=0; for(i=0;i<N;i+) if(aii=0) printf("QIYI");exit(0); printf("Jacobin"); for(k=1;k<=30;k+)

16、 for(i=0;i<N;i+) xi=yi; for(i=0;i<N;i+) t=0; for(j=0;j<N;j+) if(j!=i) t=t+aij*xj; yi=(bi-t)/aii; if(cha(x,y)<1e-6) printf("xunhuancishu:k=%dn",k); for(i=0;i<N;i+) printf("%10f",xi);printf("n"); break; if(k>30)printf("fasannn");2、实验书第4题#includ

17、e"math.h"float cha(x,y)float x3,y3;float z;int i,k,n=3;z=fabs(y0-x0);for(i=1;i<n;i+)if(fabs(yi-xi)>z) z=fabs(yi-xi);return (z);main()float a33=10,-2,-1,-2,10,-1,-1,-2,5;float b3=3,15,10,y3=0,0,0,x3;float t=0,s;int i,j,k,n=3;printf("Gauss-Seideln");for(k=1;k<=30;k+) for(i

18、=0;i<n;i+) xi=yi; for(i=0;i<n;i+) t=0; for(j=0;j<n;j+) if(j!=i) t=t+aij*xj; yi=(bi-t)/aii; if(cha(x,y)<1e-6) printf("xunhuancishu:k=%dn",k); for(i=0;i<n;i+) printf("%10f",yi); printf("n"); break; if(k>30)printf("fasannn");七、高斯-塞德尔迭代法1、通用程序#de

19、fine N 3#include"math.h"float cha(x,y)float xN,yN;float z;int i,k;z=fabs(y0-x0);for(i=1;i<N;i+) if(fabs(yi-xi)>z) z=fabs(yi-xi);return (z);main()float aNN,bN,xN,yN,h;int i,j,k;float t=0,s;for(i=0;i<N;i+) for(j=0;j<N;j+) scanf("%f",&h); aij=h; for(i=0;i<N;i+) sc

20、anf("%f",&h); bi=h;xi=0; for(i=0;i<N;i+) if(aii=0) printf("QIYI");exit(0); printf("Gauss-Seideln"); for(k=1;k<=30;k+) for(i=0;i<N;i+) yi=xi; for(i=0;i<N;i+) t=0; for(j=0;j<N;j+) if(j!=i) t=t+aij*xj; xi=(bi-t)/aii; if(cha(x,y)<1e-6) printf("xun

21、huancishu:k=%dn",k); for(i=0;i<N;i+) printf("%10f",yi);printf("n"); break; if(k>30)printf("fasannn");2、实验书第4题#include"math.h"float cha(x,y)float x3,y3;float z;int i,k,n=3;z=fabs(y0-x0);for(i=1;i<n;i+)if(fabs(yi-xi)>z) z=fabs(yi-xi);return (z);

22、main()float a33=10,-2,-1,-2,10,-1,-1,-2,5;float b3=3,15,10,x3=0,0,0,y3;float t=0,s;int i,j,k,n=3;printf("Gauss-Seideln");for(k=1;k<=30;k+) for(i=0;i<n;i+) yi=xi; for(i=0;i<n;i+) t=0; for(j=0;j<n;j+) if(j!=i) t=t+aij*xj; xi=(bi-t)/aii; if(cha(x,y)<1e-6) printf("xunhuanci

23、shu:k=%dn",k); for(i=0;i<n;i+) printf("%10f",yi); printf("n"); break; if(k>30)printf("fasannn");雅可比迭代法的算法：高斯-塞德尔迭代法的算法：八、牛顿基本插值公式（实验书第三题）main()int i,k,n;float x20,y20,t,h,p;scanf("%d",&n);for(i=0;i<=n;i+)scanf("%f%f",&xi,&yi

24、);scanf("%f",&t);for(k=1;k<=n;k+) for(i=n;i>=k;i-) yi=(yi-yi-1)/(xi-xi-k); printf("%10.5f",yi); printf("n"); p=y0;h=1;for(i=1;i<=n;i+) h=h*(t-xi-1); p+=h*yi; printf("p=%fn",p);牛顿基本插值公式算法：九、Lagarange全程插值算法（实验书第一题）main()int i,k,n;float x20,y20,t,s,p

25、;p=0;scanf("%d",&n);for(i=0;i<=n;i+)scanf("%f%f",&xi,&yi);scanf("%f",&t);for(k=0;k<=n;k+)s=1;for(i=0;i<=n;i+) if(i!=k) s=s*(t-xi)/(xk-xi); p=yk*s+p; printf("%f",p);Lagarange全程插值算法：十、复合辛普森求积公式的算法1、编制复合Simpson公式求积分的通用程序，设N=8，试算dx、#includ

26、e"math.h"float f(float x) return 1/(x*x+1);main() int i; float a=0,b=1,h,x,s,T1,T2; h=b-a; T1=h*(f(a)+f(b)/2; do s=0; x=a+h/2; s=s+f(x); T2=T1/2+h*s/2; while(fabs(T2-T1)>1e-5); 十一、多项式型经验公式算法设实验数据如下：X0.10.20.30.40.50.60.7Y5.12345.30535.56845.93786.42707.07987.94493求其二次拟合多项式#define N 7#define m 2#include "math.h"main() int i,j,k; float xN+1=0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,d,l; float yN+1=0,5.1234,5.3053,5.5684,