Proposal of efficient numerical algorithms for Jordan and Kronecker problems

2016 Fiscal Year Final Research Report

• Project/Area Number: 23560062
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Engineering fundamentals
• Research Institution: Saitama University
• Principal Investigator: SHIGEHARA Takaomi 埼玉大学, 理工学研究科, 教授 (60206084)
• Project Period (FY): 2011-04-28 – 2017-03-31
• Keywords: 数値線形代数 / ジョルダン問題 / クロネッカ問題 / 一般固有値問題

Outline of Final Research Achievements

The purpose of this work is to establish reliable numerical algorithms for the Jordan problem (JP) and Kronecker problem (KP), where not only the canonical form but transformation matrices are computed in both cases. Shedding light on a stratificated structure [see K. Kudo et al., JSIAM Letters, Vol.2 (2010) pp. 119-122 for JP and Y. Kakinuma et al., JSIAM Letters, Vol. 1 (2009) pp. 60-63 for KP], we proposed an efficient SVD-based algorithm for each problem, incorporated with the standard preprocessing reducing an input square matrix (resp. an input matrix pencil) to a block Schur form for JP (resp. a generalized upper triangular form for KP). One of the important contributions of this work from a practical viewpoint is to offer a complete numerical solution to a generalized eigenvalue problem of general type, where the associated matrix pencil might be singular.

Free Research Field

数値線形代数