Fast Algorithms for Confluent Vandermonde Linear Systems and Generalized Trummer’s Problem

Abstract

Asymptotically fast algorithms for both dual confluent Vandermonde linear systems and generalized Trummer’s problem are presented by using the divide and conquer method. It is shown that dual confluent Vandermonde linear systems can be solved in $O( n\log n\log p )$ operations and generalized Trummer’s problem can be done in $O( np\log n\log \frac{n}{p} )$ operations if fast polynomial multiplication and division are used. Also a fast algorithm for Hermite evaluation of rational functions is presented.