Question

Write a C++ code to solve linear system using triangular decomposition method.

The user will enter the input which will be 3 lines, in each line 4 values.

Answer 1

/************** LU Decomposition for solving linear equations ***********/
#include<iostream.h>
#include<conio.h>
int main()
{
    int n,i,k,j,p;
    float a[10][10],l[10][10]={0},u[10][10]={0},sum,b[10],z[10]={0},x[10]={0};
    clrscr();
    cout<<"Enter the order of matrix ! ";
    cin>>n;
    cout<<"Enter all coefficients of matrix : ";
    for(i=1;i<=n;i++)
    {
        cout<<"\nRow "<<i<<"  ";
        for(j=1;j<=n;j++)
            cin>>a[i][j];
    }
    cout<<"Enter elements of b matrix"<<endl;
    for(i=1;i<=n;i++)
        cin>>b[i];
    //********** LU decomposition *****//
    for(k=1;k<=n;k++)
    {
        u[k][k]=1;
        for(i=k;i<=n;i++)
        {
            sum=0;
            for(p=1;p<=k-1;p++)
                sum+=l[i][p]*u[p][k];
            l[i][k]=a[i][k]-sum;
        }

        for(j=k+1;j<=n;j++)
        {
            sum=0;
            for(p=1;p<=k-1;p++)
                sum+=l[k][p]*u[p][j];
            u[k][j]=(a[k][j]-sum)/l[k][k];
        }
    }
    //******** Displaying LU matrix**********//
    cout<<endl<<endl<<"LU matrix is "<<endl;
    for(i=1;i<=n;i++)
    {
        for(j=1;j<=n;j++)
            cout<<l[i][j]<<"  ";
        cout<<endl;
    }
    cout<<endl;
    for(i=1;i<=n;i++)
    {
        for(j=1;j<=n;j++)
            cout<<u[i][j]<<"  ";
        cout<<endl;
    }

    //***** FINDING Z; LZ=b*********//

    for(i=1;i<=n;i++)
    {                                        //forward subtitution method
        sum=0;
        for(p=1;p<i;p++)
        sum+=l[i][p]*z[p];
        z[i]=(b[i]-sum)/l[i][i];
    }
    //********** FINDING X; UX=Z***********//

    for(i=n;i>0;i--)
    {
        sum=0;
        for(p=n;p>i;p--)
            sum+=u[i][p]*x[p];
        x[i]=(z[i]-sum)/u[i][i];
    }
    //*********** DISPLAYING SOLUTION**************//
    cout<<endl<<"Set of solution is"<<endl;
    for(i=1;i<=n;i++)
        cout<<endl<<x[i];

    getch();
    return 0;
}