Hermite learning with gradient data

Lei Shi, Xin Guo, Ding Xuan Zhou

Research output: Journal article publicationJournal articleAcademic researchpeer-review

7 Citations (Scopus)

Abstract

The problem of learning from data involving function values and gradients is considered in a framework of least-square regularized regression in reproducing kernel Hilbert spaces. The algorithm is implemented by a linear system with the coefficient matrix involving both block matrices for generating Graph Laplacians and Hessians. The additional data for function gradients improve learning performance of the algorithm. Error analysis is done by means of sampling operators for sample error and integral operators in Sobolev spaces for approximation error.
Original languageEnglish
Pages (from-to)3046-3059
Number of pages14
JournalJournal of Computational and Applied Mathematics
Volume233
Issue number11
DOIs
Publication statusPublished - 1 Apr 2010
Externally publishedYes

Keywords

  • Hermite learning
  • Integral operator
  • Learning theory
  • Representer theorem
  • Reproducing kernel Hilbert spaces
  • Sampling operator

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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