Solve for diagonal matrix D by minimizing the operator norm in Matlab

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christina
christina 2018-12-21
评论： christina 2019-1-9
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Say that the size of matrix is ​​576x576 and size of F is1296x576.
Which matlab function can I use to solve this problem?

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Bruno Luong
Bruno Luong 2018-12-21
fminunc, fmincon and family.
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Bruno Luong
Bruno Luong 2019-1-9
编辑：Bruno Luong 2019-1-9
No. The standard math definition of VECTORIZE the matrix is
v = M(:)
M = reshape(v,[m,m])
Here
v = diag(M)
M = diag(v)
This is NOT vectorize.
FMINCON don't do anything beside minimize an objective function that user defines and provides. In the case Torsen's code
norm(A-F'*diag(D)*F,2)
is matrix 2-norm (maximum singular value).
Torsten's code is correct and do not need any modification.
You however needs to read careful the doc of fminunc, diag, norm.

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