Toeplitz systems associated with the product of a formal Laurent series and a Laurent polynomial

Abstract

A method is proposed for solving linear algebraic systems with Toeplitz matrices generated by $T ( z ) = C( z )\Phi ( z )$, where $C( z )$ is a Laurent polynomial and $\Phi ( z )$ is a formal Laurent series, and a convenient method is available for solving systems with Toeplitz matrices generated by $\Phi ( z )$. Special cases of the method provide $O( n )$ procedures for solving $n \times n$ systems with banded or rationally generated Toeplitz matrices. The latter do not require recursion with respect to n.