Algorithms for confluent Vandermonde systems

Abstract

Two compact algorithms are developed for solving systems of linear equationsV x=b andV T a=f, whereV=V(? 0,? 1, ...,? n ) is a confluent Vandermonde matrix of Hermite type. The solution is obtained by one forward and one backward vector recursion, starting with the right hand side. The total amount of storage is only ?2n. The number of arithmetic operations needed isO(n 2) and compares favourably with other proposed methods.