Algorithm for computing Jordan basis

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概要

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• We propose a novel algorithm to compute a Jordan basis (JB) for an arbitrarily given square matrix. The algorithm is based on the fact that a JB for a linear transformation $f$ is obtained by extending a JB for the restriction of $f$ to its range $R(f)$. The main ingredient of the algorithm is singular value decomposition, and that ensures backward-stability of the algorithm. To enhance the practical utility, we also introduce an automatic mechanism into the algorithm such that it outputs all possible Jordan structures close to the exact one of the input matrix.

著者

• Hashiguchi Hiroki

  Graduate School Of Science And Engineering Saitama University

• Kakinuma Yoshiaki

  NDD Corporation

• Kudo Kenji

  Graduate School of Science and Engineering, Saitama University

• Hiraoka Kazuyuki

  General Education, Wakayama National College of Technology

• Kuwajima Yutaka

  Graduate School of Science and Engineering, Saitama University

• Shigehara Takaomi

  Graduate School of Science and Engineering, Saitama University

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