A least square point of view to reproducing kernel methods to solve functional equations

In this paper we discuss and present a least square and a QR point of view to reproducing kernel methods to approximate solutions to some linear and nonlinear functional equations. The procedure we discuss here may includes ordinary, partial differential, and integral equations. We also give new pro...

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Bibliographic Details
Published inApplied mathematics and computation Vol. 357; pp. 206 - 221
Main Authors Ferreira, José Claudinei, Baquião, Maria Caruline
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.09.2019
Subjects
Approximation theory
Functional equations
Numerical methods
Positive definite kernel
Reproducing kernel
Reproducing kernel
Approximation theory
Functional equations
Positive definite kernel
Numerical methods
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Summary:In this paper we discuss and present a least square and a QR point of view to reproducing kernel methods to approximate solutions to some linear and nonlinear functional equations. The procedure we discuss here may includes ordinary, partial differential, and integral equations. We also give new proofs to some known results on this subject. The most interesting contribution is that the proposed algorithm may work even when we know a reproducing kernel but nothing more about the associated reproducing kernel Hilbert space, including the inner product structure.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2019.04.008