The Inverse of Banded Matrices

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 Br,n (1 less than or equal to r less than or equal to n) be an n x n matrix of entries {ai sub j}, -r less than or equal to r, 1 less than or equal to j less than or equal to 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 Br,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 Br,n.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2013
Accession Number
ADA576066

Entities

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  • Emrah Kilic
  • Pantelimon Stanica

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  • Naval Postgraduate School

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