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Re: Computing derivative of det(A), A singular
Posted:
Dec 8, 1996 3:44 PM
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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/
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