Singular value decomposition of weighted matrix

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If I compute the singular value decomposition of a matrix A and then want to compute the SVD of a matrix A' that is the same as A except that each row is scaled by a different number, is there a more efficient way of computing the SVD of A', given the SVD of A, than just starting from scratch?

For example, given the SVD of with elements

a11 a12
a21 a22
a31 a32

I want to efficiently compute the SVD of a matrix with elements

c1*a11 c1*a12
c2*a21 c2*a22
c3*a31 c3*a32