Efficiently computing the permanent and Hafnian of some banded Toeplitz matrices

Moshe Schwartz

doi:10.1016/j.laa.2008.10.029

Efficiently computing the permanent and Hafnian of some banded Toeplitz matrices

Moshe Schwartz

Department of Electrical & Computer Engineering

Research output: Contribution to journal › Article › peer-review

27 Scopus citations

Abstract

We present a new efficient method for computing the permanent and Hafnian of certain banded Toeplitz matrices. The method covers non-trivial cases for which previous known methods do not apply. The main idea is to use the elements of the first row and column, which determine the entire Toeplitz matrix, to construct a digraph in which certain paths correspond to permutations that the permanent and Hafnian count. Since counting paths can be done efficiently, the permanent and Hafnian for those matrices is easily obtainable.

Original language	English
Pages (from-to)	1364-1374
Number of pages	11
Journal	Linear Algebra and Its Applications
Volume	430
Issue number	4
DOIs	https://doi.org/10.1016/j.laa.2008.10.029
State	Published - 1 Feb 2009

Keywords

Banded Toeplitz matrix
Hafnian
Permanent
Toeplitz matrix

ASJC Scopus subject areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

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10.1016/j.laa.2008.10.029

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title = "Efficiently computing the permanent and Hafnian of some banded Toeplitz matrices",

abstract = "We present a new efficient method for computing the permanent and Hafnian of certain banded Toeplitz matrices. The method covers non-trivial cases for which previous known methods do not apply. The main idea is to use the elements of the first row and column, which determine the entire Toeplitz matrix, to construct a digraph in which certain paths correspond to permutations that the permanent and Hafnian count. Since counting paths can be done efficiently, the permanent and Hafnian for those matrices is easily obtainable.",

keywords = "Banded Toeplitz matrix, Hafnian, Permanent, Toeplitz matrix",

author = "Moshe Schwartz",

note = "Funding Information: This research was supported by a grant from the G.I.F., the German-Israeli Foundation for Scientific Research and Development (Grant no. 2179-1785.10/2007). E-mail address: [email protected] URL: http://www.ee.bgu.ac.il/∼schwartz 0024-3795/$ - see front matter {\textcopyright} 2008 Elsevier Inc. All rights reserved. doi:10.1016/j.laa.2008.10.029",

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PY - 2009/2/1

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N2 - We present a new efficient method for computing the permanent and Hafnian of certain banded Toeplitz matrices. The method covers non-trivial cases for which previous known methods do not apply. The main idea is to use the elements of the first row and column, which determine the entire Toeplitz matrix, to construct a digraph in which certain paths correspond to permutations that the permanent and Hafnian count. Since counting paths can be done efficiently, the permanent and Hafnian for those matrices is easily obtainable.

AB - We present a new efficient method for computing the permanent and Hafnian of certain banded Toeplitz matrices. The method covers non-trivial cases for which previous known methods do not apply. The main idea is to use the elements of the first row and column, which determine the entire Toeplitz matrix, to construct a digraph in which certain paths correspond to permutations that the permanent and Hafnian count. Since counting paths can be done efficiently, the permanent and Hafnian for those matrices is easily obtainable.

KW - Banded Toeplitz matrix

KW - Hafnian

KW - Permanent

KW - Toeplitz matrix

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DO - 10.1016/j.laa.2008.10.029

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JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 4

ER -

Efficiently computing the permanent and Hafnian of some banded Toeplitz matrices

Abstract

Keywords

ASJC Scopus subject areas

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