Numerische Mathematik

, Volume 24, Issue 1, pp 1–12

Optimally conditioned Vandermonde matrices

  • Walter Gautschi

DOI: 10.1007/BF01437212

Cite this article as:
Gautschi, W. Numer. Math. (1975) 24: 1. doi:10.1007/BF01437212


We discuss the problem of selecting the points in an (n×n) Vandermonde matrix so as to minimize the condition number of the matrix. We give numerical answers for 2≦n≦6 in the case of symmetric point configurations. We also consider points on the non-negative real line, and give numerical results forn=2 andn=3. For generaln, the problem can be formulated as a nonlinear minimax problem with nonlinear constraints or, equivalently, as a nonlinear programming problem.

Copyright information

© Springer-Verlag 1975

Authors and Affiliations

  • Walter Gautschi
    • 1
  1. 1.Computer SciencesPurdue UniversityWest LafayetteUSA

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