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arXiv · 1302.6752

The Shifting Technique for Computing the Extreme Solutions of $X + A^\top X^{-1} A = Q$

Chun-Yueh Chiang·Matthew M. Lin
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Abstract

We propose a new way for speeding up the search of the maximal solution $X_+$ of $X + A^\top X^{-1} A = Q$. It is known that the speed of convergence of traditional approaches for solving this problem depends highly on the spectral radius $\rho(X_+^{-1}A)$. If $\rho(X_+^{-1}A)$ is close to one or equal to one, the iterations of traditional approaches converges very slowly or does not converge. Our goal is to come up with a shifting tactic to remove the singularities embedded in $\rho(X_+^{-1}A)$. Finally, an example is used to demonstrate the capacity of our method.

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Chun-Yueh Chiang, Matthew M. Lin. 2013-02-27. The Shifting Technique for Computing the Extreme Solutions of $X + A^\top X^{-1} A = Q$. https://arxiv.org/abs/1302.6752

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