Suppose that Axb can be solved with Naive Gaussian Eliminati

Suppose that Ax=b can be solved with Naive Gaussian Elimination. This implies that a lower triangular matrix L with ones on its diagonal and an upper triangular matrix U exist such that A = LU.

Ax=b

(LU)x=b -Suppose A can be factored

L(Ux)=b -Move the parentheses

Ld=b -Define d = Ux

How to solve this question using MATLAB?

Solution

function x = naiv_gauss(A,b);

n = length(b); x = zeros(n,1);

for k=1:n-1 % forward elimination

for i=k+1:n

xmult = A(i,k)/A(k,k);

for j=k+1:n

A(i,j) = A(i,j)-xmult*A(k,j);

end

b(i) = b(i)-xmult*b(k);

end

end

% back substitution

x(n) = b(n)/A(n,n);

for i=n-1:-1:1

sum = b(i);

for j=i+1:n

sum = sum-A(i,j)*x(j);

end

x(i) = sum/A(i,i);

end