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https://hdl.handle.net/20.500.11851/7655
Title: | The Inverse of Banded Matrices | Authors: | Kılıç, Emrah Stanica, Pantelimon |
Keywords: | Triangular matrix Hessenberg matrix Inverse r-banded matrix |
Publisher: | Elsevier Science Bv | Abstract: | The inverses of r-banded matrices, for r = 1, 2, 3 have been thoroughly investigated as one can see from the references we provide. Let B-r,B- n(1 <= r <= n) be an n x n matrix of entries {a(j)(i)}, -r <= I <= r, 1 <= j <= r, with the remaining un-indexed entries all zeros. In this paper, generalizing a method of Mallik (1999) [5], we give the LU factorization and the inverse of the matrix B-r,B- n (if it exists). Our results are valid for an arbitrary square matrix (taking r = n), and so, we will give a new approach for computing the inverse of an invertible square matrix. Our method is based on Hessenberg submatrices associated to B-r,B-n. (c) 2012 Elsevier B.V. All rights reserved. | URI: | https://doi.org/10.1016/j.cam.2012.07.018 https://hdl.handle.net/20.500.11851/7655 |
ISSN: | 0377-0427 |
Appears in Collections: | Matematik Bölümü / Department of Mathematics Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection |
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