Numerische Mathematik

, Volume 41, Issue 2, pp 147–163

Calculation of Gauss quadratures with multiple free and fixed knots

  • G. H. Golub
  • J. Kautsky

DOI: 10.1007/BF01390210

Cite this article as:
Golub, G.H. & Kautsky, J. Numer. Math. (1983) 41: 147. doi:10.1007/BF01390210


Algorithms are derived for the evaluation of Gauss knots in the presence of fixed knots by modification of the Jacobi matrix for the weight function of the integral. Simple Gauss knots are obtained as eigenvalues of symmetric tridiagonal matrices and a rapidly converging simple iterative process, based on the merging of free and fixed knots, of quadratic convergence is presented for multiple Gauss knots. The procedures also allow for the evaluation of the weights of the quadrature corresponding to the simple Gauss knots. A new characterization of simple Gauss knots as a solution of a partial inverse eigenvalue problem is derived.

Subject Classifications

AMS (MOS): 65F15 65D30 CR: 5.14 5.16 

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • G. H. Golub
    • 1
  • J. Kautsky
    • 2
  1. 1.Department of Computer ScienceStanford UniversityStanfordUSA
  2. 2.School of Mathematical SciencesFlinders UniversityBedford ParkAustralia

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