On a collocation point of view to reproducing kernel methods

In this text, we discuss an interpolation (or a collocation) point of view to reproducing kernel methods to approximate solutions to some linear and non-linear functional equations. The proposed method allows us to avoid the usual process of orthogonalization, solving a system of algebraic equations...

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Bibliographic Details
Published inComputational & applied mathematics Vol. 40; no. 6
Main Author Ferreira, José Claudinei
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.09.2021
Springer Nature B.V
Subjects
Algorithms
Applications of Mathematics
Applied physics
Approximation
Collocation
Computational mathematics
Computational Mathematics and Numerical Analysis
Functional equations
Interpolation
Kernels
Mathematical analysis
Mathematical Applications in Computer Science
Mathematical Applications in the Physical Sciences
Mathematics
Mathematics and Statistics
Reproducing kernel
Functional equations
46E22
Numerical methods
46Cxx
Collocation methods
47Bxx
42A82
46N40
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Summary:In this text, we discuss an interpolation (or a collocation) point of view to reproducing kernel methods to approximate solutions to some linear and non-linear functional equations. The proposed method allows us to avoid the usual process of orthogonalization, solving a system of algebraic equations, with a positive defined matrix in the linear case. This also helps us to understand some methods present in the literature on this subject. We include some examples to illustrate the proposed method and an appendix with algorithms implemented in the R language.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
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ISSN:2238-3603
1807-0302
DOI:10.1007/s40314-021-01612-5