Article ID Journal Published Year Pages File Type
4603100 Linear Algebra and its Applications 2008 15 Pages PDF
Abstract

In order to estimate the condition number of the preconditioned matrix proposed in [F.R. Lin, W.K. Ching, Inverse Toeplitz preconditioners for Hermitian Toeplitz systems, Numer. Linear Algebra Appl. 12 (2005) 221–229], we study the inverse of band triangular Toeplitz matrix. We derive an explicit formula for the entries of the inverse of band lower triangular Toeplitz matrix by means of divided difference and use the formula to estimate the condition number of the preconditioned matrices. In particular, we prove that the minimal eigenvalue of preconditioned matrix is well separated from the origin.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory