On The Decay Of The Off-Diagonal Singular Values In Cyclic Reduction

It was recently observed in [10] that the singular values of the oil-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 x n block tridiagonal block Toeplitz systems with n x n quasiseparable blocks and certain generalized Sylvester equations in O(n(2) log n) arithmetic operations are shown. (c) 2016 Elsevier Inc. All rights reserved.