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

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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
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Access URL: https://zbmath.org/2068271
Accession Number: edsair.c2b0b933574d..57b6d4de91ed897e9f81bf508b9b6fe2
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  Data: The boundary curve of pseudospectrum and the stepsize control of curve tracing algorithm
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  Data: <searchLink fieldCode="AR" term="%22Liu%2C+Ying%22">Liu, Ying</searchLink><br /><searchLink fieldCode="AR" term="%22Bai%2C+Fengshan%22">Bai, Fengshan</searchLink>
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  Label: Publisher Information
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  Data: Nanjing University, Department of Mathematics, Nanjing
– Name: Subject
  Label: Subject Terms
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  Data: <searchLink fieldCode="DE" term="%22Numerical+computation+of+eigenvalues+and+eigenvectors+of+matrices%22">Numerical computation of eigenvalues and eigenvectors of matrices</searchLink><br /><searchLink fieldCode="DE" term="%22stepsize+control%22">stepsize control</searchLink><br /><searchLink fieldCode="DE" term="%22curve+tracing+algorithm%22">curve tracing algorithm</searchLink><br /><searchLink fieldCode="DE" term="%22algorithm%22">algorithm</searchLink><br /><searchLink fieldCode="DE" term="%22continuation+method%22">continuation method</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+results%22">Numerical results</searchLink><br /><searchLink fieldCode="DE" term="%22pseudospectrum%22">pseudospectrum</searchLink><br /><searchLink fieldCode="DE" term="%22prediction-correction+scheme%22">prediction-correction scheme</searchLink><br /><searchLink fieldCode="DE" term="%22bifurcation+point%22">bifurcation point</searchLink><br /><searchLink fieldCode="DE" term="%22Global+methods%2C+including+homotopy+approaches+to+the+numerical+solution+of+nonlinear+equations%22">Global methods, including homotopy approaches to the numerical solution of nonlinear equations</searchLink>
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  Label: Description
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  Data: 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.
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  Data: edsair.c2b0b933574d..57b6d4de91ed897e9f81bf508b9b6fe2
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      – Text: Undetermined
    Subjects:
      – SubjectFull: Numerical computation of eigenvalues and eigenvectors of matrices
        Type: general
      – SubjectFull: stepsize control
        Type: general
      – SubjectFull: curve tracing algorithm
        Type: general
      – SubjectFull: algorithm
        Type: general
      – SubjectFull: continuation method
        Type: general
      – SubjectFull: Numerical results
        Type: general
      – SubjectFull: pseudospectrum
        Type: general
      – SubjectFull: prediction-correction scheme
        Type: general
      – SubjectFull: bifurcation point
        Type: general
      – SubjectFull: Global methods, including homotopy approaches to the numerical solution of nonlinear equations
        Type: general
    Titles:
      – TitleFull: The boundary curve of pseudospectrum and the stepsize control of curve tracing algorithm
        Type: main
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            NameFull: Liu, Ying
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            NameFull: Bai, Fengshan
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