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Accurate Computations with Collocation and Wronskian Matrices of Jacobi Polynomials

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Abstract

In this paper an accurate method to construct the bidiagonal factorization of collocation and Wronskian matrices of Jacobi polynomials is obtained and used to compute with high relative accuracy their eigenvalues, singular values and inverses. The particular cases of collocation and Wronskian matrices of Legendre polynomials, Gegenbauer polynomials, Chebyshev polynomials of the first and second kind and rational Jacobi polynomials are considered. Numerical examples are included.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada/IUMA, Universidad de Zaragoza, Zaragoza, Spain

    E. Mainar, J. M. Peña & B. Rubio

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  1. E. Mainar
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  2. J. M. Peña
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  3. B. Rubio
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Correspondence to B. Rubio.

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This work was partially supported through the Spanish research grant PGC2018-096321-B-I00 (MCIU/AEI), by Gobierno de Aragón (E41\(\_\)17R ) and by Feder 2014-2020 “Construyendo Europa desde Aragón”.

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Mainar, E., Peña, J.M. & Rubio, B. Accurate Computations with Collocation and Wronskian Matrices of Jacobi Polynomials. J Sci Comput 87, 77 (2021). https://doi.org/10.1007/s10915-021-01500-4

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  • DOI: https://doi.org/10.1007/s10915-021-01500-4

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