Factorizations of Cauchy matrices

The development of fast algorithms for the solution of linear systems of equations with a Cauchy matrix has recently received considerable attention. Several of these algorithms factor a Cauchy matrix or its inverse into triangular and possibly diagonal matrices. The numerical properties of the factorization methods depend on the selection of pivots. This note presents elementary derivations of some factorization methods and describes a new strategy for searching both rows and columns for suitable pivots.