MODUL 2

Modul 2

Praktikum Teknik Komputasi

Sistem Persamaan Linier dengan Eliminasi GAUSS

1.     Membuat program dalam matlab untuk sistem persamaan linier dengan eliminasi GAUSS

Jawab :

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.

Jawab :

/*************** 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;

}