A fast parallel Björck-Pereyra-type algorithm for solving Cauchy linear equations (Q1970443)

This paper deals with Cauchy systems of linear equations. A new fast parallel algorithm is proposed. The new solver is an analog of the well-known Björck-Pereyra algorithm for Vandemonde systems. Numerical examples are given to illustrate the high relative accuracy. In particular, Hilbert linear systems, often considered to be to ill-conditioned to be attached, can be rapidly solved with high precision. Rounding error analysis are performed and the results indicate that for totally positive Cauchy systems the new algorithm is forward and backward stable.