A note on golden means, nonlinear matrix equations and structured doubling algorithms

Chun-Yueh Chiang, King-Wah Eric Chu, Wen-wei Lin

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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.
Original languageEnglish
Pages (from-to)955 - 972
Number of pages18
JournalTaiwanese Journal of Mathematics
Issue number3A
Publication statusPublished - 2010

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