Accurate Algorithms for Bessel Matrices
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In this paper, we prove that any collocation matrix of Bessel polynomials at positive points is strictly totally positive, that is, all its minors are positive. Moreover, an accurate method to construct the bidiagonal factorization of these matrices is obtained and used to compute with high relative accuracy the eigenvalues, singular values and inverses. Similar results for the collocation matrices for the reverse Bessel polynomials are also obtained. Numerical examples illustrating the theoretical results are included.
KeywordsBessel matrices Totally positive matrices High relative accuracy Bessel polynomials Reverse Bessel polynomials
Mathematics Subject Classification65F05 65F15 65G50 33C10 33C45 15A23
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 Aragon”.
- 15.Koev, P.: http://www.math.sjsu.edu/~koev/software/TNTool.html. Accessed November 12th (2018)