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Article

Stable Calculation of Krawtchouk Functions from Triplet Relations

Philips Research, 5656 AE Eindhoven, The Netherlands
Academic Editor: Stefano De Marchi
Mathematics 2021, 9(16), 1972; https://doi.org/10.3390/math9161972
Received: 7 June 2021 / Revised: 16 August 2021 / Accepted: 17 August 2021 / Published: 18 August 2021
(This article belongs to the Section Mathematics and Computer Science)
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. View Full-Text
Keywords: orthogonal polynomials; Krawtchouk polynomials; Krawtchouk functions; error propagation; difference equation; three-term recurrence relation orthogonal polynomials; Krawtchouk polynomials; Krawtchouk functions; error propagation; difference equation; three-term recurrence relation
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MDPI and ACS Style

den Brinker, A.C. Stable Calculation of Krawtchouk Functions from Triplet Relations. Mathematics 2021, 9, 1972. https://doi.org/10.3390/math9161972

AMA Style

den Brinker AC. Stable Calculation of Krawtchouk Functions from Triplet Relations. Mathematics. 2021; 9(16):1972. https://doi.org/10.3390/math9161972

Chicago/Turabian Style

den Brinker, Albertus C. 2021. "Stable Calculation of Krawtchouk Functions from Triplet Relations" Mathematics 9, no. 16: 1972. https://doi.org/10.3390/math9161972

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