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

Lower bounds on the condition number κp(Vc ) of a real confluent Vandermonde matrix Vc are established in terms of the dimension n or n and the largest absolute value among all nodes that define the confluent Vandermonde matrix or n and the interval that contains the nodes. In particular, it is proved that for any modest kmax (the largest number of equal nodes), κp(Vc ) behaves no smaller than On((1+ √ 2 )n), and than On((1+ √ 2 )2n) if all nodes are nonnegative. It is not clear whether those bounds are asymptotically sharp for modest kmax. This report is available on the web at http://www.ms.uky.edu/∼math/MAreport/PDF/2004-10.pdf. Department of Mathematics, University of Kentucky, Lexington, KY 40506 ([email protected].) This work was supported in part by the National Science Foundation CAREER award under Grant No. CCR-9875201.