A novel nonsymmetric \(K\)-Lanczos algorithm for the generalized nonsymmetric \(K\)-eigenvalue problems
type: Item
instance of: scholarly article
title: A novel nonsymmetric \(K\)-Lanczos algorithm for the generalized nonsymmetric \(K\)-eigenvalue problems
zbMATH Open document ID: 0888.65042
DOI: 10.1016/S0024-3795(96)00670-2
author: William R. Ferng
author: Kun-Yi Lin
author: Wen-Wei Lin
published in: Linear Algebra and its Applications
publication date: 1998-06-11T00:00:00Z
review text: The generalized eigenvalue problem \(Mx=\lambda Nx\) is studied, where the matrices \(M\), \(N\) have certain symmetries, namely the \(K_{\pm}\)-structure. A new algorithm, the nonsymmetric \(K\)-Lanczos algorithm, is developed to calculate extreme eigenvalues. For this a tridiagonalization procedure preserving the symmetries is given. It generalizes an algorithm by \textit{U. Flaschka} [Eine Variante des Lanczos-Algorithmus für große, dünn besetzte symmetrische Matrizen mit Blockstruktur, Diss. Univ. Bielefeld (1992; Zbl 0830.65023)] in the case that \(N^{-1}M\) is in addition symmetric. This algorithm can be viewed as a \(2\times 2\)-block nonsymmetric Lanczos algorithm. Numerical experiments are reported.
Mathematics Subject Classification ID: 65F15
zbMATH DE Number: 991117
zbMATH Keywords: nonsymmetric Lanczos algorithm
zbMATH Keywords: numerical experiments
zbMATH Keywords: generalized eigenvalue problem
zbMATH Keywords: extreme eigenvalues
zbMATH Keywords: tridiagonalization
reviewed by: Ludwig Elsner
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 991117