Sistem Persamaan Linier dengan Eliminasi GAUSS
1. Membuat program dalam matlab untuk sistem persamaan
linier dengan
eliminasi GAUSS
function x=gaussian(A,b);
n=length(b);
x=zeros(n,1);
for k=1:n-1
for i=k+1:n
m=A(i,k)/A(k,k);
for j=k:n
A(i,j)=A(i,j)-m*A(k,j);
end
b(i)=b(i)-m*b(k);
end
end
%solusi
x(n)=b(n)/A(n,n);
for i=n-1:-1:1
for j=i+1:n
b(i)=b(i)-A(i,j)*x(j);
end
x(i)=b(i)/A(i,i);
end
2. Membuat Program
dalam Java/C++/C#/PHP untuk sistem persamaan linier dengan eliminasi gauss
/*************** Gauss Jordan method ********************/
#include<iostream.h>
#include<conio.h>
int main()
{
int i,j,k,n;
float a[10][10],d;
clrscr();
cout<<"No of equations ? ";cin>>n;
cout<<"Read all coefficients of matrix with b matrix too
"<<endl;
for(i=1;i<=n;i++) // read nxn matrix - cofficients
for(j=1;j<=n+1;j++)
cin>>a[i][j];
/**************
partial pivoting **************/
for(i=n;i>1;i--)
{
if(a[i-1][1]<a[i][1])
for(j=1;j<=n+1;j++)
{
d=a[i][j];
a[i][j]=a[i-1][j];
a[i-1][j]=d;
}
}
cout<<"pivoted output: "<<endl;
for(i=1;i<=n;i++)
{
for(j=1;j<=n+1;j++)
cout<<a[i][j]<<"
";
cout<<endl;
}
/**********
reducing to diagonal matrix ***********/
for(i=1;i<=n;i++)
{
for(j=1;j<=n;j++)
if(j!=i)
{
d=a[j][i]/a[i][i];
for(k=1;k<=n+1;k++)
a[j][k]-=a[i][k]*d;
}
}
/**************
reducing to unit matrix *************/
for(i=1;i<=n;i++)
{
d=a[i][i];
for(j=1;j<=n+1;j++)
a[i][j]=a[i][j]/d;
}
cout<<"your solutions: "<<endl;
for(i=1;i<=n;i++)
{
for(j=1;j<=n+1;j++)
cout<<a[i][j]<<"
";
cout<<endl;
}
getch();
return 0;
}
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