Taiwanese Journal of Mathematics


Chun-Yueh Chiang, Eric King-Wah Chu, and 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.

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Taiwanese J. Math., Volume 14, Number 3A (2010), 955-972.

First available in Project Euclid: 18 July 2017

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Primary: 15A24: Matrix equations and identities 65F99: None of the above, but in this section

algebraic Riccati equation condition nonlinear matrix equation matrix golden mean structured doubling algorithm


Chiang, Chun-Yueh; Chu, Eric King-Wah; Lin, Wen-Wei. A NOTE ON GOLDEN MEANS, NONLINEAR MATRIX EQUATIONS AND STRUCTURED DOUBLING ALGORITHMS. Taiwanese J. Math. 14 (2010), no. 3A, 955--972. doi:10.11650/twjm/1500405876. https://projecteuclid.org/euclid.twjm/1500405876

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