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KIAM Preprint № 71, Moscow, 2019
Authors: Bakhvalov P.A., Surnachev M.D.
On transformation of the stable matrices to a block-diagonal form
Abstract:
We consider square matrices A such that ||exp(tA)||<=K for all t>=0. We show that each matrix possessing this property can be transformed to a block-diagonal form such shat condition numbers of all the digaonal blocks and the transformation matrix depend only on K and matrix size. The obtained result is applied to the analysis of long-time simulation accuracy of difference schemes.
Keywords:
similarity of matrices, Kreiss theorem, superconvergence, long-time simulation accuracy
Publication language: russian,  pages: 15
Research direction:
Mathematical problems and theory of numerical methods
Russian source text:
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About authors:
  • Bakhvalov Pavel Alexeevisch,  orcid.org/0000-0003-3416-8277KIAM RAS
  • Surnachev Mikhail Dmitriyevich,  orcid.org/0000-0003-4071-5097KIAM RAS