×

zbMATH — the first resource for mathematics

Collected matrix derivative results for forward and reverse mode algorithmic differentiation. (English) Zbl 1154.65308
Bischof, Christian H. (ed.) et al., Advances in automatic differentiation. Selected papers based on the presentations at the 5th international conference on automatic differentiation, Bonn, Germany, August 11–15, 2008. Berlin: Springer (ISBN 978-3-540-68935-5/pbk). Lecture Notes in Computational Science and Engineering 64, 35-44 (2008).
Summary: This paper collects together a number of matrix derivative results which are very useful in forward and reverse mode algorithmic differentiation. It highlights in particular the remarkable contribution of P. S. Dwyer and M. S. MacPhail [Ann. Math. Stat. 19, 517–534 (1948; Zbl 0032.00103)] which derives the linear and adjoint sensitivities of a matrix product, inverse and determinant, and a number of related results motivated by applications in multivariate analysis in statistics.
For the entire collection see [Zbl 1143.65003].

MSC:
65D25 Numerical differentiation
Software:
ADMAT; ADMIT; MAD; MATLAB expm
PDF BibTeX XML Cite