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The boundary curve of pseudospectrum and the stepsize control of curve tracing algorithm

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Bibliographic Details
Title: The boundary curve of pseudospectrum and the stepsize control of curve tracing algorithm
Authors: Liu, Ying, Bai, Fengshan
Publisher Information: Nanjing University, Department of Mathematics, Nanjing
Subject Terms: Numerical computation of eigenvalues and eigenvectors of matrices, stepsize control, curve tracing algorithm, algorithm, continuation method, Numerical results, pseudospectrum, prediction-correction scheme, bifurcation point, Global methods, including homotopy approaches to the numerical solution of nonlinear equations
Description: Summary: The boundary curve of the pseudospectrum is defined as a contour line of its resolvent norm. The curve tracing algorithm is a rather simple continuation method, which determines this curve by a prediction-correction scheme. But this algorithm can not deal with the bifurcation point where the resolvent norm is not differentiable. Due to this defect we investigate the smoothness of the boundary curve, and give a method of stepsize control which can deal with bifurcation points. Numerical results are also presented.
Document Type: Article
File Description: application/xml
Access URL: https://zbmath.org/2068271
Accession Number: edsair.c2b0b933574d..57b6d4de91ed897e9f81bf508b9b6fe2
Database: OpenAIRE
Description
Abstract:Summary: The boundary curve of the pseudospectrum is defined as a contour line of its resolvent norm. The curve tracing algorithm is a rather simple continuation method, which determines this curve by a prediction-correction scheme. But this algorithm can not deal with the bifurcation point where the resolvent norm is not differentiable. Due to this defect we investigate the smoothness of the boundary curve, and give a method of stepsize control which can deal with bifurcation points. Numerical results are also presented.