Split algorithms for skewsymmetric Toeplitz matrices with arbitrary rank profile
A skewsymmetric Toeplitz matrix has the form \(T_N=[a_{i-j}]_{i,j=1}^N\) with \(a_{-j}=-a_j\). A general linear system \(T_Nf=b\) with a nonsingular Toeplitz matrix can be solved `fast' with complexity \(O(n^2)\) using Levinson-type or Schur-type algorithms. However, these require that all leading principal submatrices are nonsingular which rules out all skewsymmetric Toeplitz matrices. In a previous paper [Oper. Theory Adv. Appl. 135, 193--208 (2002; Zbl 1022.65028)] the authors obtained a fast algorithm for the case of centro-nonsingular matrices. In the present paper they generalize this to all nonsingular skewsymmetric Toeplitz matrices. Their algorithm is related to generalizations of \(ZW\) and \(WZ\) factorizations of matrices.
scientific article; zbMATH DE number 2083139
scientific article