It was recently observed in  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 queuing models. In this paper, we provide a theoretical bound to the basis of this exponential decay together with a tool for its estimation based on a rational interpolation problem. Numerical experiments show that the bound is often accurate in practice. Applications to solving n × n block tridiagonal block Toeplitz systems with n × n quasiseparable blocks and certain generalized Sylvester equations in O(n 2 log n) arithmetic operations are shown.
|Autori:||Bini, Dario Andrea; Massei, Stefano; Robol, Leonardo|
|Titolo:||On the decay of the off-diagonal singular values in cyclic reduction|
|Anno del prodotto:||2017|
|Digital Object Identifier (DOI):||10.1016/j.laa.2016.12.027|
|Appare nelle tipologie:||1.1 Articolo in rivista|