Summary
Formulas, or close two-sided estimates, are given for the norm of the inverse of a Vandermonde matrix when the constituent parameters are arranged in certain symmetric configurations in the complex plane. The effect of scaling the parameters is also investigated. Asymptotic estimates of the respective condition numbers are derived in special cases.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bettis, D. G.: Numerical integration of products of Fourier and ordinary polynomials. Numer. Math.14, 421–434 (1970)
Gautschi, W.: On inverses of Vandermonde and confluent Vandermonde matrices. Numer. Math.4, 117–123 (1962)
Singhal, K., Vlach, J.: Accuracy and speed of real and complex interpolation. Computing11, 147–158 (1973)
Szegö, G.: Orthogonal polynomials, 2nd rev. ed., Amer. Math. Soc. Colloq. Publ., Vol.23, Amer. Math. Soc., Providence, R. I., 1959
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Gautschi, W. Norm estimates for inverses of Vandermonde matrices. Numer. Math. 23, 337–347 (1974). https://doi.org/10.1007/BF01438260
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01438260