Abstract
With a well-known formulation of matrix permanent by a multivariate polynomial, algorithms for the computation of the matrix permanent are considered in terms of automatic differentiation, where a succinct program with a C++ template for the higher order derivatives is described. A special set of commutative quadratic nilpotent elements is introduced, and it is shown that the permanent can be computed efficiently as a variation of implementation of higher order automatic differentiation. Given several ways for transforming the multivariate polynomial into univariate polynomials, six algorithms that compute the value of the permanent are described with their computational complexities. One of the complexities is O(n2n), the same as that of the most popular Ryser’s algorithm.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer
About this paper
Cite this paper
Kubota, K. (2006). Computation of Matrix Permanent with Automatic Differentiation. In: Bücker, M., Corliss, G., Naumann, U., Hovland, P., Norris, B. (eds) Automatic Differentiation: Applications, Theory, and Implementations. Lecture Notes in Computational Science and Engineering, vol 50. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-28438-9_6
Download citation
DOI: https://doi.org/10.1007/3-540-28438-9_6
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28403-1
Online ISBN: 978-3-540-28438-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)