Question

MATLAB script Gaussian Elimination without pivoting, not working no matter what I try.

So far my script is :

function [x] = myGauss( A, b )

n = size(A,1); % getting n
Ab = [A,b];      % produces the augmented matrix
x = zeros(n,1); % solution
fprintf('Augmented matrix \n')

%FORWARD ELIMINATION  

for k=1:n-1
    for i=k+1:n
        lambda = A(i,k)/A(k,k);
        for j=k+1:n
            A(i,j) = A(i,j) - lambda*A(k,j);
        end;
        b(i) = b(i) - lambda*b(i)
    end;
end;

%Backwards substitution

x(n) = b(n) / A(n,n);
for k = n-1:1
    for j = k+1: n
        sums = b(k) - A(k,j) * x(j);
    end
    x(k) = sums / A(k,k);
end

and to launch it I have:

%Question 1:
A = [2, -4, -1;
    1, -3, 1;
    3, -5, -3]

b = [1; 1; 1];

x = myGauss( A, b )

Any highly appreciated.

Answer 1

Corrected script:

function y=myyygauss(M, Y)
[m,n] = size (M);
D = [M Y];
for j = 1:n-1
for i = j+1:m
T = D(i,j)/D(j,j);
D(i,j:n+1) = D(i,j:n+1)-T*D(j,j:n+1);
end
end
x = zeros(m,1);
x(m) =D(m,n+1)/D(m,m);
for i = m-1:-1:1
x(i) = (D(i,n+1)-D(i,i+1:n)*x(i+1:n))/D(i,i);
end
y=x
end

To use the above script:

a1=[1 2 3;-4 5 6; -7 8 9];
a2=[10 20 30]';
a=myyygauss(a1,a2);

Output:

>> a
a =

0.00000
0.00000
3.33333

_____________________________________________________________

sample 2:

a1=[1 -2 -3;-4 5 6; -7 8 -9];
a2=[10 20 30]';
a=myyygauss(a1,a2);

output:

>> a
a =

-31.1111
-22.2222
1.1111

____________________________________________________________________________________

But for the given matrix A, the determinant value is equal to 0.Gauss elimination method can be applied only for linear set of equations. If the det ==0 , then the set of equations say that the system is non linear.

>> A = [2, -4, -1;
1, -3, 1;
3, -5, -3]
A =

2 -4 -1
1 -3 1
3 -5 -3

>> det(A)
ans = -8.8818e-16

This is almost equal to zero. Hence the solution cannot be obtained. But the script will work for all the linear set of equations.

Before applying gauss elimination method or any other method to find the solution of linear equations, check whether the determinant is zero or not.