[Numpy-discussion] On the difference of two positive definite matrices

Charles R Harris charlesr.harris@gmail....
Sun Dec 16 19:38:43 CST 2012


On Sun, Dec 16, 2012 at 6:20 PM, Virgil Stokes <vs@it.uu.se> wrote:

> Suppose I have two positive definite matrices, A and B. Is it possible
> to use U*D*U^T  factorizations of these matrices to obtain a numerically
> stable result for their difference, A - B ?
>
> My application is the "UD" factorization method for the Kalman filter
> followed by the Rauch-Tung-Striebel smoother --- this is where the
> difference of two positive definite matrices occurs.
>
> I hope that this question is appropriate for this list and does not
> offend any subscribers.
>
>
Not sure what you are asking, but there is a coordinate system in which
they are both diagonal. Nevertheless, the difference may not be positive
definite.

Chuck
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