Efficient handling of complex shift parameters in the low-rank Cholesky factor ADI method
type: Item
instance of: scholarly article
title: Efficient handling of complex shift parameters in the low-rank Cholesky factor ADI method
zbMATH Open document ID: 1267.65047
author: P. Benner
author: Patrick Kürschner
author: J. Saak
published in: Numerical Algorithms
publication date: 2013-02-15T00:00:00Z
review text: A new formulation of the low-rank Cholesky factor version of the alternating directions (ADI) implicit method is given. The proposed method generates real low-rank factors. It makes use of the dependence of iterates to complex conjugate shift parameters. This formulation reduces by half the amount of storage requirements and number of arithmetic calculations. Numerical results are given to show that the proposed algorithm is superior to the other presently known methods. The proposed method is tested on generalized Lyapunov and algebraic Riccati equations with large and sparse matrices and is also found superior in these instances.
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 65F50
zbMATH DE Number: 6136617
zbMATH Keywords: matrix equations
zbMATH Keywords: algorithmic enhancement
zbMATH Keywords: Cholesky factorization
zbMATH Keywords: Lyapunov equation
zbMATH Keywords: alternating directions (ADI) implicit method
zbMATH Keywords: numerical results
zbMATH Keywords: algorithm
zbMATH Keywords: algebraic Riccati equation
zbMATH Keywords: sparse matrices
Wikidata QID: Q115214689
reviewed by: R. P. Tewarson
describes a project that uses: toms/782
describes a project that uses: LYAPACK
describes a project that uses: Algorithm 432
describes a project that uses: CSparse
describes a project that uses: RRQR
MaRDI profile type: Publication
full work available at URL: s11075-012-9569-7
OpenAlex ID: W2076656421
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DOI: 10.1007/S11075-012-9569-7
description: scientific article; zbMATH DE number 6136617