Differentiation of Kaltofen's division-free determinant algorithm

Details Differentiation of Kaltofen's division-free determinant algorithm Differentiation of Kaltofen's division-free determinant algorithm

2008-04-07

arxiv.org/abs/0804.1021v1

Journal of Symbolic Computation 7, 46 (2011) 773-790

Computer Science

Symbolic Computation

Scientific paper

10.1016/j.jsc.2010.08.012

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.

Affiliated with

Also associated with

No associations

Rating

Differentiation of Kaltofen's division-free determinant algorithm does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Differentiation of Kaltofen's division-free determinant algorithm, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Differentiation of Kaltofen's division-free determinant algorithm will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-729903