Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5773206 | Linear Algebra and its Applications | 2017 | 27 Pages |
Abstract
It was recently observed in [10] 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 nÃn block tridiagonal block Toeplitz systems with nÃn quasiseparable blocks and certain generalized Sylvester equations in O(n2logâ¡n) arithmetic operations are shown.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Dario A. Bini, Stefano Massei, Leonardo Robol,