Krylov methods and determinants for detecting bifurcations in one parameter dependent partial differential equations
type: Item
instance of: scholarly article
title: Krylov methods and determinants for detecting bifurcations in one parameter dependent partial differential equations
zbMATH Open document ID: 1111.65112
author: N. E. Zubov
published in: BIT
publication date: 2007-01-05T00:00:00Z
review text: The authors study the computation of the sign of the determinant for a large matrix as a byproduct of the preconditioned generalized minimal residual (GMRES) method when applied to solve the linear systems arising in the discretization of partial differential equations. Numerical experiments are presented where the technique is applied to detect and locate pitchfork and transcritical bifurcation points on a one parameter dependent system. With an appropriate selection of the initial guess in the GMRES method, the technique is shown to detect and accurately locate bifurcation points. The authors have also presented an analysis that helps to explain the good performance observed in practice. A conclusion and some remarks are included at the end of the paper.
Mathematics Subject Classification ID: 65P30
Mathematics Subject Classification ID: 65F40
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 37G10
Mathematics Subject Classification ID: 65F35
zbMATH DE Number: 5081850
zbMATH Keywords: determinant
zbMATH Keywords: Arnoldi decomposition
zbMATH Keywords: compact operator
zbMATH Keywords: Hilbert space
zbMATH Keywords: spectral method
zbMATH Keywords: partial differential equation
zbMATH Keywords: continuation method
zbMATH Keywords: bifurcation location
zbMATH Keywords: preconditioning
zbMATH Keywords: Krylov subspace method
zbMATH Keywords: generalized minimal residual method
zbMATH Keywords: numerical experiments
reviewed by: Hassane Bouzahir
describes a project that uses: LOCA
describes a project that uses: PLTMG
describes a project that uses: PLTMGC
MaRDI profile type: Publication
full work available at URL: s10543-006-0101-0
OpenAlex ID: W2086353207
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DOI: 10.1007/S10543-006-0101-0
description: scientific article; zbMATH DE number 5081850