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Stable Calculation of Krawtchouk Functions from Triplet Relations

Author

Listed:
  • Albertus C. den Brinker

    (Philips Research, 5656 AE Eindhoven, The Netherlands)

Abstract

Deployment of the recurrence relation or difference equation to generate discrete classical orthogonal polynomials is vulnerable to error propagation. This issue is addressed for the case of Krawtchouk functions, i.e., the orthonormal basis derived from the Krawtchouk polynomials. An algorithm is proposed for stable determination of these functions. This is achieved by defining proper initial points for the start of the recursions, balancing the order of the direction in which recursions are executed and adaptively restricting the range over which equations are applied. The adaptation is controlled by a user-specified deviation from unit norm. The theoretical background is given, the algorithmic concept is explained and the effect of controlled accuracy is demonstrated by examples.

Suggested Citation

  • Albertus C. den Brinker, 2021. "Stable Calculation of Krawtchouk Functions from Triplet Relations," Mathematics, MDPI, vol. 9(16), pages 1-9, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:16:p:1972-:d:616505
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