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A recursive relation for the determinant of a pentadiagonal matrix

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Roland A. SweetAuthors Info & Claims

Communications of the ACM, Volume 12, Issue 6

Pages 330 - 332

https://doi.org/10.1145/363011.363152

Published: 01 June 1969 Publication History

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Abstract

A recursive relation, relating leading principal minors, is developed for the determinant of a pentadiagonal matrix. A numerical example is included to indicate its use in calculating eigenvalues.

Reference

[1]

MAYBEE, J. S., AND QUIRK, J. Qualitative problems in matrix theory. To appear in SIAM Rev.

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Pickmann-Soto HArela-Pérez SLozano CNina H(2024)Realization of Extremal Spectral Data by Pentadiagonal MatricesMathematics10.3390/math1214219812:14(2198)Online publication date: 12-Jul-2024
https://doi.org/10.3390/math12142198
Evans EFrancis A(2022)Algorithmic techniques for finding resistance distances on structured graphsDiscrete Applied Mathematics10.1016/j.dam.2022.04.012320(387-407)Online publication date: Oct-2022
https://doi.org/10.1016/j.dam.2022.04.012
Losonczi L(2021)Determinants of some pentadiagonal matricesGlasnik Matematicki10.3336/gm.56.2.0556:2(271-286)Online publication date: 23-Dec-2021
https://doi.org/10.3336/gm.56.2.05
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Index Terms

A recursive relation for the determinant of a pentadiagonal matrix
1. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
      1. Computations on matrices

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Published In

Communications of the ACM Volume 12, Issue 6

June 1969

85 pages

ISSN:0001-0782

EISSN:1557-7317

DOI:10.1145/363011

Editor:
M. Stuart Lynn
IBM Research Center, Houston, TX

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Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 June 1969

Published in CACM Volume 12, Issue 6

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Pickmann-Soto HArela-Pérez SLozano CNina H(2024)Realization of Extremal Spectral Data by Pentadiagonal MatricesMathematics10.3390/math1214219812:14(2198)Online publication date: 12-Jul-2024
https://doi.org/10.3390/math12142198
Evans EFrancis A(2022)Algorithmic techniques for finding resistance distances on structured graphsDiscrete Applied Mathematics10.1016/j.dam.2022.04.012320(387-407)Online publication date: Oct-2022
https://doi.org/10.1016/j.dam.2022.04.012
Losonczi L(2021)Determinants of some pentadiagonal matricesGlasnik Matematicki10.3336/gm.56.2.0556:2(271-286)Online publication date: 23-Dec-2021
https://doi.org/10.3336/gm.56.2.05
Kurmanbek BErlangga YAmanbek Y(2021)Explicit inverse of near Toeplitz pentadiagonal matrices related to higher order difference operatorsResults in Applied Mathematics10.1016/j.rinam.2021.10016411(100164)Online publication date: Aug-2021
https://doi.org/10.1016/j.rinam.2021.100164
Shitov Y(2021)The determinants of certain (0,1) Toeplitz matricesLinear Algebra and its Applications10.1016/j.laa.2021.02.002618(150-157)Online publication date: Jun-2021
https://doi.org/10.1016/j.laa.2021.02.002
Losonczi L(2021)Eigenpairs of some imperfect pentadiagonal Toeplitz matricesLinear Algebra and its Applications10.1016/j.laa.2020.09.014608(282-298)Online publication date: Jan-2021
https://doi.org/10.1016/j.laa.2020.09.014
Alvarez MBrondani AFrança FC. L(2020)Characteristic Polynomials and Eigenvalues for Certain Classes of Pentadiagonal MatricesMathematics10.3390/math80710568:7(1056)Online publication date: 1-Jul-2020
https://doi.org/10.3390/math8071056
Anđelić Mda Fonseca C(2020)Some determinantal considerations for pentadiagonal matricesLinear and Multilinear Algebra10.1080/03081087.2019.170884569:16(3121-3129)Online publication date: 6-Jan-2020
https://doi.org/10.1080/03081087.2019.1708845
Khasanah NFarikhin Surarso B(2017)The Algorithm of Determinant Centrosymmetric Matrix Based on Lower Hessenberg FormJournal of Physics: Conference Series10.1088/1742-6596/824/1/012028824(012028)Online publication date: 18-Apr-2017
https://doi.org/10.1088/1742-6596/824/1/012028
Jia JLi S(2017)On determinants of cyclic pentadiagonal matrices with Toeplitz structureComputers & Mathematics with Applications10.1016/j.camwa.2016.11.03173:2(304-309)Online publication date: 15-Jan-2017
https://dl.acm.org/doi/10.1016/j.camwa.2016.11.031
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Some results on determinants and inverses of nonsingular pentadiagonal matrices

An explicit formula for the inverse of a pentadiagonal Toeplitz matrix

An elementary algorithm for computing the determinant of pentadiagonal Toeplitz matrices

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