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PAT – a Reliable Path-Following Algorithm

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Abstract

This paper presents a new technique for the reliable computation of the σ-pseudospectrum defined by Λσ(A)={z∈C : σmin(A−zI)≤σ} where σmin is the smallest singular value. The proposed algorithm builds an orbit of adjacent equilateral triangles to capture the level curve ϒσ(A)={z∈C : σmin(A−zI)=σ} and uses a bisection procedure on specific triangle vertices to compute a numerical approximation to ϒσ. The method is guaranteed to terminate, even in the presence of round-off errors.

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Authors and Affiliations

  1. ESIB-USJ, Campus des Sciences et Technologies, Beirut, Lebanon

    Dany Mezher

  2. IRISA-INRIA, Campus de Beaulieu, 35042, Rennes cedex, France

    Bernard Philippe

Authors
  1. Dany Mezher
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  2. Bernard Philippe
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Mezher, D., Philippe, B. PAT – a Reliable Path-Following Algorithm. Numerical Algorithms 29, 131–152 (2002). https://doi.org/10.1023/A:1014824425949

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  • DOI: https://doi.org/10.1023/A:1014824425949

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