Recursive solution of Cauchy-Vandermonde systems of equations (Q1805194)

This paper presents two types of recursive algorithms for the solution of linear systems \(Ax = b\) the coefficient matrix of which consists of a Cauchy and a Vandermonde matrix part. The computational amount for both type I and type II of recursive algorithms is \(O(n^2)\) in sequential computation. In parallel processing the amount for type I is \(O(n \log n)\), and for type II is \(O(n)\). The last section considers nonsquare systems and shows that the recursive algorithm can also be applied in this situation.