10个重要的算法C语言实现源代码：拉格朗日_牛顿插值_高斯_龙贝格

10个重要的算法C语言实现源代码：拉格朗日，牛顿插值，高斯，龙贝格~~

关键字: 拉格朗日，牛顿插值，高斯，龙贝格 1.拉格朗日插值多项式 ，用于离散数据的拟合

C/C++ code

#include #include #include

float lagrange(float *x,float *y,float xx,int n) /*拉格朗日插值算法*/

{ int i,j;

float *a,yy=0.0; /*a作为临时变量，记录拉格朗日插值多项式*/ a=(float *)malloc(n*sizeof(float)); for(i=0;i<=n-1;i++) { a[i]=y[i];

for(j=0;j<=n-1;j++)

if(j!=i) a[i]*=(xx-x[j])/(x[i]-x[j]); yy+=a[i]; }

free(a); return yy; }

main() { int i,n;

float x[20],y[20],xx,yy; printf(\"Input n:\"); scanf(\"%d\if(n>=20) {printf(\"Error!The value of n must in (0,20).\"); getch();return 1;}

if(n<=0) {printf(\"Error! The value of n must in (0,20).\"); getch(); return 1;}

for(i=0;i<=n-1;i++) { printf(\"x[%d]:\ scanf(\"%f\}

printf(\"\\n\");

for(i=0;i<=n-1;i++)

{ printf(\"y[%d]:\printf(\"\\n\");

printf(\"Input xx:\");

scanf(\"%f\

yy=lagrange(x,y,xx,n);

printf(\"x=%f,y=%f\\n\getch(); }

2.牛顿插值多项式，用于离散数据的拟合

C/C++ code

#include #include #include

void difference(float *x,float *y,int n) { float *f; int k,i;

f=(float *)malloc(n*sizeof(float)); for(k=1;k<=n;k++) { f[0]=y[k];

for(i=0;if[i+1]=(f[i]-y[i])/(x[k]-x[i]); y[k]=f[k]; }

return; }

main() { int i,n;

float x[20],y[20],xx,yy; printf(\"Input n:\"); scanf(\"%d\

if(n>=20) {printf(\"Error! The value of n must in (0,20).\"); getch(); return 1;} if(n<=0) {printf(\"Error! The value of n must in (0,20).\");getch(); return 1;}

for(i=0;i<=n-1;i++) { printf(\"x[%d]:\ scanf(\"%f\}

printf(\"\\n\"); for(i=0;i<=n-1;i++)

{ printf(\"y[%d]:\printf(\"\\n\");

difference(x,(float *)y,n);

printf(\"Input xx:\"); scanf(\"%f\yy=y[20];

for(i=n-1;i>=0;i--) yy=yy*(xx-x[i])+y[i]; printf(\"NewtonInter(%f)=%f\getch(); }

3.高斯列主元消去法,求解其次线性方程组

C/C++ code

#include #include #define N 20 int main()

{ int n,i,j,k; int mi,tmp,mx;

float a[N][N],b[N],x[N]; printf(\"\\nInput n:\"); scanf(\"%d\if(n>N)

{ printf(\"The input n should in(0,N)!\\n\"); getch(); return 1; }

if(n<=0)

{ printf(\"The input n should in(0,N)!\\n\"); getch(); return 1; }

printf(\"Now input a(i,j),i,j=0...%d:\\n\for(i=0;iscanf(\"%f\

printf(\"Now input b(i),i,j=0...%d:\\n\for(i=0;i{ for(j=i+1,mi=i,mx=fabs(a[i][j]);jmx) { mi=j;

mx=fabs(a[j][i]);

}

if(i{ tmp=b[i];b[i]=b[mi];b[mi]=tmp; for(j=i;ja[i][j]=a[mi][j]; a[mi][j]=tmp; } }

for(j=i+1;j{ tmp=-a[j][i]/a[i][i]; b[j]+=b[i]*tmp; for(k=i;ka[j][k]+=a[i][k]*tmp; } }

x[n-1]=b[n-1]/a[n-1][n-1]; for(i=n-2;i>=0;i--) { x[i]=b[i];

for(j=i+1;jfor(i=0;iprintf(\"Answer:\\n x[%d]=%f\\n\getch(); return 0; }

#include #include #define NUMBER 20 #define Esc 0x1b #define Enter 0x0d

float A[NUMBER][NUMBER+1] ,ark; int flag,n;

exchange(int r,int k); float max(int k); message();

main() {

float x[NUMBER]; int r,k,i,j; char celect; clrscr();

printf(\"\\n\\nUse Gauss.\");

printf(\"\\n\\n1.Jie please press Enter.\"); printf(\"\\n\\n2.Exit press Esc.\"); celect=getch(); if(celect==Esc) exit(0);

printf(\"\\n\\n input n=\"); scanf(\"%d\

printf(\" \\n\\nInput matrix A and B:\"); for(i=1;i<=n;i++) {

printf(\"\\n\\nInput a%d1--a%d%d and b%d:\

for(j=1;j<=n+1;j++) scanf(\"%f\ }

for(k=1;k<=n-1;k++) {

ark=max(k);

if(ark==0) {

printf(\"\\n\\nIt's wrong!\");message(); }

else if(flag!=k) exchange(flag,k); for(i=k+1;i<=n;i++) for(j=k+1;j<=n+1;j++)

A[i][j]=A[i][j]-A[k][j]*A[i][k]/A[k][k]; }

x[n]=A[n][n+1]/A[n][n]; for( k=n-1;k>=1;k--) {

float me=0;

for(j=k+1;j<=n;j++) {

me=me+A[k][j]*x[j]; }

x[k]=(A[k][n+1]-me)/A[k][k]; }

for(i=1;i<=n;i++)

{

printf(\" \\n\\nx%d=%f\ }

message(); }

exchange(int r,int k) {

int i;

for(i=1;i<=n+1;i++) A[0][i]=A[r][i]; for(i=1;i<=n+1;i++) A[r][i]=A[k][i]; for(i=1;i<=n+1;i++) A[k][i]=A[0][i]; }

float max(int k) {

int i;

float temp=0; for(i=k;i<=n;i++)

if(fabs(A[i][k])>temp) {

temp=fabs(A[i][k]); flag=i; }

return temp; }

message() {

printf(\"\\n\\n Go on Enter ,Exit press Esc!\"); switch(getch()) {

case Enter: main(); case Esc: exit(0);

default:{printf(\"\\n\\nInput error!\");message();} } }

4.龙贝格求积公式，求解定积分

C/C++ code

#include #include

#define f(x) (sin(x)/x) #define N 20

#define MAX 20 #define a 2 #define b 4

#define e 0.00001

float LBG(float p,float q,int n) { int i;

float sum=0,h=(q-p)/n; for (i=1;isum+=(f(p)+f(q))/2; return(h*sum); }

void main() { int i;

int n=N,m=0;

float T[MAX+1][2]; T[0][1]=LBG(a,b,n); n*=2;

for(m=1;mfor(i=1;i<=m;i++)

T[i][1]=T[i-1][1]+(T[i-1][1]-T[i-1][0])/(pow(2,2*m)-1); if((T[m-1][1]T[m][1]-e)) { printf(\"Answer=%f\\n\ return ; } } }

C/C++ code

5.牛顿迭代公式，求方程的近似解

C/C++ code

#include #include #include #define N 100 #define PS 1e-5 #define TA 1e-5

float Newton(float (*f)(float),float(*f1)(float),float x0 ) { float x1,d=0; int k=0; do

{ x1= x0-f(x0)/f1(x0);

if((k++>N)||(fabs(f1(x1))d=(fabs(x1)<1?x1-x0:(x1-x0)/x1); x0=x1;

printf(\"x(%d)=%f\\n\}

while((fabs(d))>PS&&fabs(f(x1))>TA) ; return x1; }

float f(float x)

{ return x*x*x+x*x-3*x-3; } float f1(float x)

{ return 3.0*x*x+2*x-3; } void main()

{ float f(float); float f1(float); float x0,y0;

printf(\"Input x0: \"); scanf(\"%f\

printf(\"x(0)=%f\\n\y0=Newton(f,f1,x0);

printf(\"\\nThe root is x=%f\\n\getch(); }

6. 牛顿-科特斯求积公式，求定积分

C/C++ code

#include #include int NC(a,h,n,r,f) float (*a)[]; float h; int n,f; float *r; { int nn,i; float ds;

if(n>1000||n<2) { if (f)

printf(\"\\n Faild! Check if 1if(n==2)

{ *r=0.5*((*a)[0]+(*a)[1])*(h); return(0); }

if (n-4==0) { *r=0;

*r=*r+0.375*(h)*((*a)[n-4]+3*(*a)[n-3]+3*(*a)[n-2]+(*a)[n-1]); return(0); }

if(n/2-(n-1)/2<=0) nn=n; else nn=n-3;

ds=(*a)[0]-(*a)[nn-1]; for(i=2;i<=nn;i=i+2)

ds=ds+4*(*a)[i-1]+2*(*a)[i]; *r=ds*(h)/3; if(n>nn)

*r=*r+0.375*(h)*((*a)[n-4]+3*(*a)[n-3]+3*(*a)[n-2]+(*a)[n-1]); return(0); }

main() {

float h,r; int n,ntf,f; int i;

float a[16];

printf(\"Input the x[i](16):\\n\"); for(i=0;i<=15;i++)

scanf(\"%d\h=0.2; f=0;

ntf=NC(a,h,n,&r,f); if(ntf==0)

printf(\"\\nR=%f\\n\ else

printf(\"\\n Wrong!Return code=%d\\n\ getch(); }

7.雅克比迭代，求解方程近似解

C/C++ code

#include #include #define N 20 #define MAX 100 #define e 0.00001 int main() { int n; int i,j,k; float t;

float a[N][N],b[N][N],c[N],g[N],x[N],h[N]; printf(\"\\nInput dim of n:\"); scanf(\"%d\if(n>N)

{ printf(\"Faild! Check if 0{printf(\"Faild! Check if 0scanf(\"%f\

printf(\"Input c[i],i=0…%d:\\n\for(i=0;i{ b[i][j]=-a[i][j]/a[i][i]; g[i]=c[i]/a[i][i]; } for(i=0;i{ for(k=0;k{ if(j==k) continue; h[j]+=b[j][k]*x[k]; } } t=0;

for(j=0;jif(t{ printf(\"x_i=\\n\"); for(i=0;iprintf(\"after %d repeat , return\\n\ getch(); return 1; }

getch(); }

8.秦九昭算法

C/C++ code

#include

float qin(float a[],int n,float x) { float r=0; int i;

for(i=n;i>=0;i--) r=r*x+a[i]; return r; }

main()

{ float a[50],x,r=0; int n,i; do

{ printf(\"Input frequency:\"); scanf(\"%d\ }

while(n<1);

printf(\"Input value:\");

for(i=0;i<=n;i++) scanf(\"%f\

printf(\"Input frequency:\"); scanf(\"%f\ r=qin(a,n,x);

printf(\"Answer:%f\ getch(); }

9.幂法

C/C++ code

#include #include #define N 100 #define e 0.00001 #define n 3

float x[n]={0,0,1};

float a[n][n]={{2,3,2},{10,3,4},{3,6,1}}; float y[n]; main()

{ int i,j,k; float xm,oxm; oxm=0;

for(k=0;kfor(i=0;ixm=0;

for(j=0;jif(fabs(y[j])>xm) xm=fabs(y[j]); for(j=0;jfor(j=0;jif(fabs(xm-oxm){ printf(\"max:%f\\n\\n\ printf(\"v[i]:\\n\");

for(k=0;k}

oxm=xm; } getch(); }

10.高斯塞德尔

C/C++ code

#include #include #define N 20 #define M 99 float a[N][N]; float b[N]; int main()

{ int i,j,k,n;

float sum,no,d,s,x[N];

printf(\"\\nInput dim of n:\"); scanf(\"%d\if(n>N)

{ printf(\"Faild! Check if 0if(n<=0)

{ printf(\"Faild! Check if 0scanf(\"%f\

printf(\"Input b[i],i=0…%d:\\n\for(i=0;iprintf(\"\\nk=%dx=\

for(i=0;i{ k++;

if(k>M){printf(\"\\nError!\\n”);getch();} break; }

no=0.0;

for(i=0;ifor(j=0;jif (j!=i) sum=sum+a[i][j]*x[j]; x[i]=(b[i]-sum)/a[i][i]; d=fabs(x[i]-s); if (noprintf(\"\\nk=%2dx=\

for(i=0;iwhile (no>=0.1e-6); if(no<0.1e-6)

{ printf(\"\\n\\n answer=\\n\"); printf(\"\\nk=%d\ for (i=0;iprintf(\"\\n x[%d]=%12.8f\}

getch(); }