Hello!
Assuming that B is a square matrices with real entries, I am looking for a matrix A, with complex (but preferably real) entries, which minimizes:
limn -> inf || An - B ||F
where || ||F denotes the Frobenius (i.e., Euclidian) norm.
As a bonus, I am ready to settle for near-optimality of the minimum, as long as computing A is computationally efficient.
Thank you very much for your help!
Hi, do you have any additional constraint on A (diagonal for example).
I ask the question because for example A=B is solution of Min norm_F(A-B) (cas n = 1) and leads to a zero residual.
Dear Richard,
I know how to solve the problem for finite n, however, I don't know know how to handle the case for n -> infinity.
Hi, do you have an analytical expression of the minimum for finite n?
I would just compute the eigendecomposition of B as Q * D * Q-1, and then I would have A = Q * D.^(1/n) * Q-1, such that An = B.
You may look for a projection A such that ||A-B||F is minimum. This takes care of the limit.
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