What are the numerical method of gauss elimination and gauss Jordan method?

Answer 1

Here is the program for Gauss elimination method

#include<iostream.h>

#include<conio.h>

#include<math.h>

void main()

{float a[6][6],b[6],x[6],t,s;

int i,j,n,k;

clrscr();

cout<<"Enter the maximum no. of matrix"<<endl;

cin>>n;

cout<<"Enter th elements of matrix"<<endl;

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

{

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

{

cin>>a[i][j];

}

}

cout<<"enter the right constant"<<endl;

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

{

cin>>b[i];

}

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

{

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

{

t=a[i][k]/a[k][k];

a[i][k]=0;

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

{

a[i][j]=a[i][j]-(t*a[k][i]);

}

b[i]=b[i]-(t*b[k]);

}

}

x[n-1]=b[n-1]/a[n-1][n-1];

for(i=n-1;i>=0;i--)

{

s=0;

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

{s=s+(a[i][j]*x[j]);

}

x[i]=(b[i]-s)/a[i][i];

}

cout<<"the solution is"<<endl;

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

{

cout<<"x["<<i<<"]="<<x[i]<<endl;

}

getch();

}

C program for Gauss Jordan method:

#include<iostream.h>

#include<conio.h>

#include<math.h>

void main()

{float a[6][6],b[6],x[6],t,s;

int i,j,n,k;

clrscr();

cout<<"Enter the maximum no. of matrix"<<endl;

cin>>n;

cout<<"Enter th elements of matrix"<<endl;

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

{

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

{

cin>>a[i][j];

}

}

cout<<"enter the right constant"<<endl;

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

{

cin>>a[i][n];

}

for(k=0;k<n;k++)

{

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

if(i!=k)

{

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

{

a[i][j]=a[i][j]-(a[i][k]/a[k][k])*a[k][j]);

cout<<"the solution is"<<endl;

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

{

x[i]=(a[i][n]/a[i][i]);

cout<<"x["<<i<<"]="<<x[i]<<endl;

}

getch();

}