A fast factorization algorithm for a confluent Cauchy matrix

Abstract

This paper presents a fast factorization algorithm for con°uent Cauchy-like matrices. The algorithm consists of two parts. First, a con°uent Cauchy-like matrix is transformed into a Cauchy-like matrix available to pivot without changing its structure. Sec-ond, a fast partial pivoting factorization algorithm for the Cauchy-like matrix is presented. A new displacement structure cannot pos-sibly generate all entries of a transformed matrix, which is called by "partially reconstructible". This paper also discusses how the pro-posed factorization algorithm can be generally applied to partially reconstructive matrices.