Lower bounds for the condition number of Vandermonde matrices |
| |
| Authors: | Walter Gautschi Gabriele Inglese |
| |
| Institution: | (1) Department of Computer Sciences, Purdue University, 47907 West Lafavette, IN, USA;(2) CNR-Istituto Analisi Globale e Applicazioni, Via S. Marta 13/A, I-50139 Florence, Italy |
| |
| Abstract: | Summary We derive lower bounds for the  -condition number of then×n-Vandermonde matrixV
n(x) in the cases where the node vectorx
T=x1, x2,...,xn] has positive elements or real elements located symmetrically with respect to the origin. The bounds obtained grow exponentially inn. withO(2n) andO(2n/2), respectively. We also compute the optimal spectral condition numbers ofV
n(x) for the two node configurations (including the optimal nodes) and compare them with the bounds obtained.Dedicated to the memory of James H. WilkinsonSupported, in part, by the National Science Foundation under grant CCR-8704404 |
| |
| Keywords: | AMS (MOS): 15A12 49D15 65F35 CR: G1 3 G1 6 |
| 本文献已被 SpringerLink 等数据库收录！ |
|
