NDLI: Multiscale Support Vector Approach for Solving Ill-Posed Problems

Content Provider	Springer Nature Link
Author	Zhong, Min Hon, Yiu Chung Lu, Shuai
Copyright Year	2014
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 $$\epsilon $$ -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.
Starting Page	317
Ending Page	340
Page Count	24
File Format	PDF
ISSN	08857474
Journal	Journal of Scientific Computing
Volume Number	64
Issue Number	2
e-ISSN	15737691
Language	English
Publisher	Springer US
Publisher Date	2014-10-21
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Multiscale support vector approach Compactly supported radial basis functions Ill-posed problems Regularization methods Inverse problems Ill-posed problems, regularization Improperly posed problems; regularization Algorithms Computational Mathematics and Numerical Analysis ApplicationMathematics/Computational Methods of Engineering Theoretical, Mathematical and Computational Physics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Theoretical Computer Science Engineering Computational Theory and Mathematics Computational Mathematics Numerical Analysis Software

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