Remember that
so the function can be written as
Its Frechet derivative easily now equals
(also there's a minus in your formula that I can't relate to anything).
So, for the second derivative, differentiate
Hi, I am new to the forum. I work on control engineering and want to calculate the second order Frechet derivative of f(X)=P(I-XP)^(-1) with respect to X, X and P being positive semidefinite matrices. I tried to compute the first order one, which is -P(I-XP)^(-1)K(I-XP)^(-1), but have no idea on how to calculate the second order one... Thanks for help.
Remember that
so the function can be written as
Its Frechet derivative easily now equals
(also there's a minus in your formula that I can't relate to anything).
So, for the second derivative, differentiate