Numerische Mathematik

, Volume 61, Issue 1, pp 409–432

The eigenvalues of Hermite and rational spectral differentiation matrices

  • J. A. C. Weideman

DOI: 10.1007/BF01385518

Cite this article as:
Weideman, J.A.C. Numer. Math. (1992) 61: 409. doi:10.1007/BF01385518


We derive expressions for the eigenvalues of spectral differentiation matrices for unbounded domains. In particular, we consider Galerkin and collocation methods based on Hermite functions as well as rational functions (a Fourier series combined with a cotangent mapping). We show that (i) first derivative matrices have purely imaginary eigenvalues and second derivative matrices have real and negative eigenvalues, (ii) for the Hermite method the eigenvalues are determined by the roots of the Hermite polynomials and for the rational method they are determined by the Laguerre polynomials, and (iii) the Hermite method has attractive stability properties in the sense of small condition numbers and spectral radii.

Mathematics Subject Classification (1991)

65M10 65D25 65F15 42C10 

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • J. A. C. Weideman
    • 1
  1. 1.Department of MathematicsOregon State UniversityCorvallisUSA

Personalised recommendations