Accurate and efficient computations with Wronskian matrices of Bernstein and related bases

In this article, we provide a bidiagonal decomposition of the Wronskian matrices of Bernstein bases of polynomials and other related bases such as the Bernstein basis of negative degree or the negative binomial basis. The mentioned bidiagonal decompositions are used to achieve algebraic computations...

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Bibliographic Details
Published inNumerical linear algebra with applications Vol. 29; no. 3
Main Authors Mainar, Esmeralda, Peña, Juan M., Rubio, Beatriz
Format Journal Article
LanguageEnglish
Published Oxford Wiley Subscription Services, Inc 01.05.2022
Subjects
accurate computations
Bernstein bases
bidiagonal decompositions
collocation matrices
Decomposition
Eigenvalues
Linear systems
Mathematical analysis
negative binomial basis
Polynomials
Wronskian matrices
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Summary:In this article, we provide a bidiagonal decomposition of the Wronskian matrices of Bernstein bases of polynomials and other related bases such as the Bernstein basis of negative degree or the negative binomial basis. The mentioned bidiagonal decompositions are used to achieve algebraic computations with high relative accuracy for these Wronskian matrices. The numerical experiments illustrate the accuracy obtained using the proposed decomposition when computing inverse matrices, eigenvalues or singular values, and the solution of some related linear systems.
Bibliography:Funding information
Gobierno de Aragón, E41_20R; MCUI/IEA, PGC2018‐096321‐B‐I00
ISSN:1070-5325
1099-1506
DOI:10.1002/nla.2423