Hello,

I would like to minimize and find the zeros of the function F(S,P)=trace(S-SP’(A+ PSP’)^-1PS) in respect to S and P.

S is symmetric square matrix.

P is a rectangular matrix

Could you help me?

Thank you very much

All the best

GoodSpirit

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- Jan 23rd 2013, 05:41 AMGoodSpiritmatrix trace minimizations and zeros
Hello,

I would like to minimize and find the zeros of the function F(S,P)=trace(S-SP’(A+ PSP’)^-1PS) in respect to S and P.

S is symmetric square matrix.

P is a rectangular matrix

Could you help me?

Thank you very much

All the best

GoodSpirit - Jan 24th 2013, 03:54 AMGoodSpiritRe: matrix trace minimizations and zeros
Hello everybody,

Perhaps I should explain a little bit.

The aim is to minimize an error metric and preferentially drive it to zero.

This should be done as function of S and P, as function of their rank and dimensions.

By the way, the matrix A is symmetric too.

Many thanks

Best regards

GoodSpirit - Jan 25th 2013, 03:36 AMGoodSpiritRe: matrix trace minimization and zeros
Hello again,

I forgot to say that P' and S' are the transpose of P and S respectively.

and ^-1 is the inverse operation.

I've been using matrix derivatives...

What do you think about that? :)

best regards

GoodSpirit