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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 dX/dX is : XX^{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 LAPACKetalcompatible 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/



