標題: A NOTE ON GOLDEN MEANS, NONLINEAR MATRIX EQUATIONS AND STRUCTURED DOUBLING ALGORITHMS
作者: Chiang, Chun-Yueh
Chu, Eric King-Wah
Lin, Wen-Wei
應用數學系
Department of Applied Mathematics
關鍵字: Algebraic Riccati equation;Condition;Nonlinear matrix equation;Matrix golden mean;Structured doubling algorithm
公開日期: 1-Jun-2010
摘要: Several beautiful formulae for the solutions of some nonlinear matrix equations were proposed by Yongdo Lim in 2007, in terms of the matrix golden means. Numerically, these formulae will not be applicable when some matrices involved are ill-conditioned. In this note, we propose to partially fill in this gap of applicability with the structured doubling algorithm, under some favourable conditions. We also discuss how some pre-processing or scaling procedures can be applied to the matrix equations, to improve their condition. More generally, we also explore the possibility of computing the matrix golden mean using structured doubling algorithms. Some numerical examples will be presented for illustrative purposes.
URI: http://hdl.handle.net/11536/5364
ISSN: 1027-5487
期刊: TAIWANESE JOURNAL OF MATHEMATICS
Volume: 14
Issue: 3A
起始頁: 955
結束頁: 972
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