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Matrix Calculus-Based Approach to Orthogonal Polynomial Sequences

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Abstract

In this paper, an approach to orthogonal polynomials based on matrix calculus is proposed. Known and new basic results are given, such as recurrence relations and determinant forms. New algorithms, similar, but not identical, to the Chebyshev one, for practical calculation of the polynomials are presented. The cases of monic and symmetric orthogonal polynomial sequences and the case of orthonormal polynomial sequences have been considered. Some classical and non-classical examples are given. The work is framed in a broader perspective, already started by the authors. It provides for the determination of properties of a general sequence of polynomials and, therefore, their applicability to special classes of the most important polynomials.

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Acknowledgements

The authors would like to thank anonymous referees for their valuable comments. One of the authors wishes to thank the support of INdAM-GNCS project 2019.

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  1. Department of Mathematics and Computer Science, University of Calabria, 87036, Rende (CS), Italy

    F. A. Costabile, M. I. Gualtieri & A. Napoli

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  1. F. A. Costabile
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  2. M. I. Gualtieri
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  3. A. Napoli
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Correspondence to A. Napoli.

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Costabile, F.A., Gualtieri, M.I. & Napoli, A. Matrix Calculus-Based Approach to Orthogonal Polynomial Sequences. Mediterr. J. Math. 17, 118 (2020). https://doi.org/10.1007/s00009-020-01555-x

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