An algorithm for generating interpolatory quadrature rules of the highest degree of precision with preassigned nodes for general weight functions

ABSTRACT

The construction of an algorithm is described for generating interpolatory quadrature rules of the highest degree of precision with arbitrarily preassigned nodes for general constant signed weight functions. It is of very wide application in that to operate, only the definition of the 3-term recurrence relation for the orthogonal polynomials associated with the weight function need be supplied. The algorithm can be used to produce specific individual quadrature rules or sequences of rules by iterative application.

REFERENCES

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INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.4 Quadrature and Numerical Differentiation
          Subjects: Gaussian quadrature

Additional Classification:
  F. Theory of Computation
  F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY
      F.2.1 Numerical Algorithms and Problems
          Subjects: Computations on polynomials

  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS

General Terms:
Algorithms