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Topic: Computing derivative of det(A), A singular
Replies: 1   Last Post: Dec 8, 1996 3:44 PM

 Matt Kennel Posts: 10 Registered: 12/7/04
Re: Computing derivative of det(A), A singular
Posted: Dec 8, 1996 3:44 PM

John Hench (smshenc@rdg.ac.uk) wrote:
: I'd like to add to this discussion some references
: concerning matrix derivaties. They are "Matrix
: Derivatives" by Gerald Rogers and "Kronecker
: Products and Matrix Calculus" with Applications by
: A. Graham.

: BTW, Graham's book mentions that d|X|/dX is
: |X|X^{-1}, which is just the adj(X), so the
: question is how do you accurately compute the
: adjugate of a matrix, right?

Usually given matrix formulae with inverses the best way to
numerically solve them is to rewrite as a system of equations
in LAPACK-et-al-compatible form without explicit inverses.

e.g. if the desired quantity Q is

Q = |X| X^{-1}

rewrite as

Q*X = |X|

and solve for Q with whatever library routine is appropriate. Often
they want the unknown multiplied on the right, so take transposes:

X^T * Q^T = |X|^T

{ A * UNKNOWN = B } (standard LAPACK template)

solve for Q^T, giving Q after post processing.

--
Matthew B. Kennel/mbk@caffeine.engr.utk.edu/I do not speak for ORNL, DOE or UT
Oak Ridge National Laboratory/University of Tennessee, Knoxville, TN USA/