## Taiwanese Journal of Mathematics

### A NOTE ON GOLDEN MEANS, NONLINEAR MATRIX EQUATIONS AND STRUCTURED DOUBLING ALGORITHMS

#### Abstract

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.

#### Article information

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

Dates
First available in Project Euclid: 18 July 2017

https://projecteuclid.org/euclid.twjm/1500405876

Digital Object Identifier
doi:10.11650/twjm/1500405876

Mathematical Reviews number (MathSciNet)
MR2667726

Zentralblatt MATH identifier
1226.65032

#### Citation

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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