A Lanczos–like reduction of symmetric structured matrices to semiseparable form*

Abstract

An algorithm that transforms symmetric matrices to similar semiseparable ones was recently proposed [19]. As with the Householder reduction, the latter algorithm works without taking into account the structure of the original matrix. In this paper we propose a Lanczos–like algorithm to transform a symmetric matrix to a similar semiseparable one by making use of a product of the original matrix times a vector at each step. An efficient algorithm can be achieved if the original matrix is sparse or structured.