Gaussian Elimination algorithm is not properly partial pivoting

Arata Kaizaki

2019 10 11

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11 次查看（30 天）

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Hello, I am working through some practice exercises for MatLab practice and one of the problems ask me to include partial pivoting to a previous problem that asks to write an algorithm for Gaussian Elimination (which I have done). Here's what I have so far:

r = RandStream('mt19937ar','Seed',1234);
A = r.randn(6,7);
n = 6;
out = [];
for ii = 1:n-1 
    [m,t] = max(abs(A));
    
    if A(ii,ii) < m(1,ii)
        temp = A(ii,:);
        A(ii,:) = A(t(1,ii),:);
        A(t(1,ii),:) = temp;
    else 
        for j = ii+1:n
        if A(ii,ii) == 0
            print('Method failed: matrix is rank deficient');
        else
            A(j,:) = A(j,:) - (A(j,ii)/A(ii,ii))*A(ii,:);
        end
        end
    end
    out = vertcat(t4_out,A);
end

The input is a matrix A that is n x m (m >= n) and the output should be an n x m upper triangular matrix. At the end of each iteration, I have a matrix A(i) with zeros below the diagonal on the ith column and I would need to construct the matrix [A(1), A(2), ..., A(n-1)] (hence the use of vertcat) and the output should be a 30x7 matrix. I tried my best to implement partial pivoting, but my output doesn't end up being an upper triangular matrix. I don't really get what's wrong with my partial pivoting code. Without the partial pivoting, my regular Gaussian Elimination algorithm still works and I get an upper triangular matrix. Can someone help me figure out why my partial pivoting code doesn't get me to an upper triangular matrix? Any help will be appreciated.