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An analytical approach: Explicit inverses of periodic tridiagonal matrices

Hopkins, Tim, Kılıç, Emrah (2018) An analytical approach: Explicit inverses of periodic tridiagonal matrices. Journal of Computational and Applied Mathematics, 335 . pp. 207-226. ISSN 0377-0427. (doi:10.1016/j.cam.2017.11.038)

Abstract

We derive an explicit formula for the inverse of a general, periodic, tridiagonal matrix. Our approach is to derive its factorization using backward continued fractions (BCF) which are an essential tool in number theory. We then use these formulae to construct an algorithm for inverting a general, periodic, tridiagonal matrix which we implement in Maple.1 Finally, we present the results of testing the efficiency of our new algorithm against another published implementation and against the library procedures available within Maple to invert a general matrix and to compute its determinant.

Item Type: Article
DOI/Identification number: 10.1016/j.cam.2017.11.038
Uncontrolled keywords: Matrix inversion, LU-Factorization, Inverse, Backward continued fraction
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Sciences > School of Computing
Depositing User: Tim Hopkins
Date Deposited: 11 May 2018 15:10 UTC
Last Modified: 09 Aug 2019 10:25 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/66997 (The current URI for this page, for reference purposes)
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