A reducing approach for symmetrically sparse banded and anti-banded matrices

• Type: Article in International Scientific Journal
• Date: 2019

Authors

Bebiano, N (Author) Other; Susana Borges Furtado (Author) FEP

Journal

Title: Linear Algebra and Its Applications

Vol. 581

Pages: 36-50

ISSN: 0024-3795

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 5 Citations

Scopus - 5 Citations

Other information

Authenticus ID: P-00Q-T3H

DOI: 10.1016/j.laa.2019.07.006

Abstract (EN): In this paper we consider sparse symmetrically banded matrices in which the nonzero off-diagonals are positioned a multiple of k steps from the main diagonal. We show that such a matrix T is permutationally similar to direct sum of banded matrices. In particular, when T has exactly one nonzero off-diagonal above and below the main diagonal, the direct summands are tridiagonal. If T has a w-Toeplitz structure, the blocks are w'-Toeplitz, with w' = 1cm(w, k)/k. This reduction allows the study of spectral properties of T from those of the direct summands. Finally, we give a reduction of sparse symmetrically banded matrices relatively to the main antidiagonal.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 15