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| Код |
//////////////////////////////////////////////////////////////////////////////
//
// Solving system of linear equations (Zaidel method)
// (c) Johna Smith, 1996
//
// Method description:
// Given: system of linear equations
// a11 x1 + a12 x2 + ... + a1n xn = b1
// a21 x1 + a22 x2 + ... + a2n xn = b2
// ...
// an1 x1 + an2 x2 + ... + ann xn = bn
//
// We use following iterative formula to solve this system:
//
// 1 i-1 N
// xi(j+1)=xi(j)- --- ( SUM aik xk(j+1) + SUM aik xk(j) -bi)
// aii k=1 k=i
//
// where xi(j+1) is j+1-th iteration, xi(j) is j-th iteration
//
//////////////////////////////////////////////////////////////////////////////
#include <stdio.h>
#include <math.h>
#define N 3 // size of matrix
#define N1 N+1
float matrix[N][N1]=
{{10,1,1,12},
{2,10,1,13},
{2,2,10,14}
};
float z[N]={0,0,0}; // first iteration
float epsilon=0.0001; // required accuracy
void ShowMatrix(void)
{
for (int i=0;i<N;i++)
{
for (int j=0;j<N;j++)
printf("%+f*x%d",matrix[i][j],i+1);
printf("=%f\n",matrix[i][N]);
}
}
void main(void)
{
// Variables declaration
float x[N];
short int i,j;
int iterations=0,finish=0;
// Printing given matrix
ShowMatrix();
while (!finish)
{
finish=1;
for (i=0;i<N;i++)
{
x[i]=-matrix[i][N];
for (j=0;j<N;j++) x[i]+=matrix[i][j]*z[j];
// don't stop iterations until required accuracy is reached
if (fabs(x[i]/matrix[i][i])>=epsilon) finish=0;
x[i]=z[i]-x[i]/matrix[i][i];
// next iteration
z[i]=x[i];
}
iterations++;
}
// Printing solution
printf("\nSolution:\n");
for (i=0;i<N;i++)
printf("x%d=%f\n",i+1,x[i]);
printf("%d iterations were made",iterations);
}
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