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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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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Abstract 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.
AbstractList 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.
Author Mainar, Esmeralda
Rubio, Beatriz
Peña, Juan M.
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  surname: Rubio
  fullname: Rubio, Beatriz
  email: brubio@unizar.es
  organization: Universidad de Zaragoza
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10.1063/1.4893216
10.1016/0024-3795(87)90313-2
10.1016/j.amc.2005.05.049
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10.1137/S0895479803438225
10.1016/S0167-8396(99)00015-1
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10.1016/j.laa.2006.11.020
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10.1002/nla.2295
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10.1017/S0962492906350015
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Snippet In this article, we provide a bidiagonal decomposition of the Wronskian matrices of Bernstein bases of polynomials and other related bases such as the...
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crossref
wiley
SourceType Aggregation Database
Publisher
SubjectTerms accurate computations
Bernstein bases
bidiagonal decompositions
collocation matrices
Decomposition
Eigenvalues
Linear systems
Mathematical analysis
negative binomial basis
Polynomials
Wronskian matrices
Title Accurate and efficient computations with Wronskian matrices of Bernstein and related bases
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