Matrix displacement decompositions and applications to Toeplitz linear systems

Using the approach of Bozzo, Di Fiore, and Zellini, new matrix displacement decomposition formulas are introduced. It is shown how an arbitrary square matrix A can be expressed as sums of products of Hessenberg algebra matrices and high level (block) matrices whose submatrices are Hessenberg algebra matrices and have variable sizes. In most cases these block factors are block-diagonal matrices. Then these formulas are used in sequential and parallel solution of Toeplitz systems.