Multiscale Support Vector Approach for Solving Ill-Posed Problems

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

4 Scopus Citations
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Author(s)

  • Min Zhong
  • Yiu Chung Hon
  • Shuai Lu

Related Research Unit(s)

Detail(s)

Original languageEnglish
Pages (from-to)317-340
Journal / PublicationJournal of Scientific Computing
Volume64
Issue number2
Online published21 Oct 2014
Publication statusPublished - Aug 2015

Abstract

Based on the use of compactly supported radial basis functions, we extend in this paper the support vector approach to a multiscale support vector approach (MSVA) scheme for approximating the solution of a moderately ill-posed problem on bounded domain. The Vapnik’s ϵ -intensive function is adopted to replace the standard l 2 loss function in using the regularization technique to reduce the error induced by noisy data. Convergence proof for the case of noise-free data is then derived under an appropriate choice of the Vapnik’s cut-off parameter and the regularization parameter. For noisy data case, we demonstrate that a corresponding choice for the Vapnik’s cut-off parameter gives the same order of error estimate as both the a posteriori strategy based on discrepancy principle and the noise-free a priori strategy. Numerical examples are constructed to verify the efficiency of the proposed MSVA approach and the effectiveness of the parameter choices.

Research Area(s)

  • Multiscale support vector approach, Compactly supported radial basis functions, Ill-posed problems, Regularization methods, RADIAL BASIS FUNCTIONS, PARTIAL-DIFFERENTIAL-EQUATIONS, KERNEL HILBERT-SPACE, TIKHONOV REGULARIZATION, INVERSE PROBLEMS, SOBOLEV SPACES, CAUCHY-PROBLEM, COLLOCATION, REGRESSION, ALGORITHM

Citation Format(s)

Multiscale Support Vector Approach for Solving Ill-Posed Problems. / Zhong, Min; Hon, Yiu Chung; Lu, Shuai.
In: Journal of Scientific Computing, Vol. 64, No. 2, 08.2015, p. 317-340.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review