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arXiv · 1608.01567

On the decay of the off-diagonal singular values in cyclic reduction

Dario Andrea Bini·Stefano Massei·Leonardo Robol
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Abstract

It was recently observed that the singular values of the off-diagonal blocks of the matrix sequences generated by the Cyclic Reduction algorithm decay exponentially. This property was used to solve, with a higher efficiency, certain quadratic matrix equations encountered in the analysis of queueing models. In this paper, we provide a sharp theoretical bound to the basis of this exponential decay together with a tool for its estimation based on a rational interpolation problem. Applications to solving $n\times n$ block tridiagonal block Toeplitz systems with $n\times n$ semiseparable blocks and certain generalized Sylvester equations in $O(n^2\log n)$ arithmetic operations are shown.

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Dario Andrea Bini, Stefano Massei, Leonardo Robol. 2016-08-04. On the decay of the off-diagonal singular values in cyclic reduction. https://doi.org/10.1016/j.laa.2016.12.027

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