Lower bounds for the condition number of a real confluent Vandermonde matrix

Author:
Ren-Cang Li

Journal:
Math. Comp. **75** (2006), 1987-1995

MSC (2000):
Primary 15A12, 65F35

DOI:
https://doi.org/10.1090/S0025-5718-06-01856-4

Published electronically:
May 16, 2006

MathSciNet review:
2240645

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Lower bounds on the condition number of a real confluent Vandermonde matrix are established in terms of the dimension , or and the largest absolute value among all nodes that define the confluent Vandermonde matrix and the interval that contains the nodes. In particular, it is proved that for any modest (the largest multiplicity of distinct nodes), behaves no smaller than , or than if all nodes are nonnegative. It is not clear whether those bounds are asymptotically sharp for modest .

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Additional Information

**Ren-Cang Li**

Affiliation:
Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506

Email:
rcli@ms.uky.edu

DOI:
https://doi.org/10.1090/S0025-5718-06-01856-4

Keywords:
Optimal condition number,
Vandermonde matrix,
confluent Vandermonde matrix,
Chebyshev polynomials

Received by editor(s):
October 20, 2004

Received by editor(s) in revised form:
May 23, 2005

Published electronically:
May 16, 2006

Additional Notes:
This work was supported in part by the National Science Foundation CAREER award under Grant No. CCR-9875201 and by the National Science Foundation under Grant No. DMS-0510664.

Article copyright:
© Copyright 2006
American Mathematical Society