Direct and inverse eigenvalue problems for diagonal-plus-semiseparable matrices
type: Item
instance of: scholarly article
title: Direct and inverse eigenvalue problems for diagonal-plus-semiseparable matrices
zbMATH Open document ID: 1053.65025
author: Dario Fasino
author: L. Gemignani
published in: Numerical Algorithms
publication date: 2004-01-14T00:00:00Z
review text: A special congruence transformation is introduced for computing the eigenvalues of diagonal-plus-semiseparable (DPSS) matrices which allows the evaluation of the characteristic polynomial in linear time and the direct application of a divide and conquer eigenvalue solver to the DPSS matrix without any preliminary reduction. The inverse eigenvalue problem is then solved to reconstruct the symmetric DPSS matrix from its spectrum and some other information. The results are applied for the QR factorization of special Cauchy matrices.
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 65F18
zbMATH DE Number: 2026782
zbMATH Keywords: semiseparable matrices
zbMATH Keywords: band matrices
zbMATH Keywords: eigenvalue problems
zbMATH Keywords: congruence transformation
zbMATH Keywords: inverse eigenvalue problem
zbMATH Keywords: QR factorization
zbMATH Keywords: Cauchy matrices
reviewed by: F. Szidarovszky
MaRDI profile type: Publication
DOI: 10.1023/B:NUMA.0000005402.66868.AF
description: scientific article; zbMATH DE number 2026782