Differentiation of Kaltofen's division-free determinant algorithm
Abstract
Kaltofen has proposed a new approach in [Kaltofen 1992] for computing matrix determinants. The algorithm is based on a baby steps/giant steps construction of Krylov subspaces, and computes the determinant as the constant term of a characteristic polynomial. For matrices over an abstract field and by the results of Baur and Strassen 1983, the determinant algorithm, actually a straight-line program, leads to an algorithm with the same complexity for computing the adjoint of a matrix [Kaltofen 1992]. However, the latter is obtained by the reverse mode of automatic differentiation and somehow is not ``explicit''. We study this adjoint algorithm, show how it can be implemented (without resorting to an automatic transformation), and demonstrate its use on polynomial matrices.
Keywords
Cite
@article{arxiv.0804.1021,
title = {Differentiation of Kaltofen's division-free determinant algorithm},
author = {Gilles Villard},
journal= {arXiv preprint arXiv:0804.1021},
year = {2011}
}