A Lanczos-type algorithm for the QR factorization of regular Cauchy matrices

We present a fast algorithm for computing the QR factorization of Cauchy matrices with real nodes. The algorithm works for almost any input matrix, does not require squaring the matrix, and fully exploits the displacement structure of Cauchy matrices. We prove that, if the determinant of a certain semiseparable matrix is non-zero, a three term recurrence relation among the rows or columns of the factors exists. Copyright © 2002 John Wiley & Sons, Ltd.