# Confluent Vandermonde matrices using Sylvester's structure

Abstract : In this paper, we first show that a confluent Vandermonde matrix may be viewed as composed of some rows of a certain block Vandermonde matrix. As a result, we derive a Sylvester's structure for this class of matrices that appears as a natural generalization of the straightforward one known for usual Vandermonde matrices. Then we present some applications as an illustration of the established structure. For example, we show how confluent Vandermonde and Hankel matrices are linked with each other, and also we describe an O($n^{2}$) algorithm for solving confluent Vandermonde least squares minimizations problems.
Keywords :
Document type :
Reports
Domain :
Complete list of metadatas

Cited literature [21 references]

https://hal-lara.archives-ouvertes.fr/hal-02102110
Contributor : Colette Orange <>
Submitted on : Wednesday, April 17, 2019 - 9:14:32 AM
Last modification on : Wednesday, November 20, 2019 - 3:14:33 AM

### File

RR1998-16.pdf
Files produced by the author(s)

### Identifiers

• HAL Id : hal-02102110, version 1

### Citation

Lamine Melkemi. Confluent Vandermonde matrices using Sylvester's structure. [Research Report] LIP RR-1998-16, Laboratoire de l'informatique du parallélisme. 1998, 2+14p. ⟨hal-02102110⟩

Record views