Using compactly supported radial basis functions (CSRBFs) of varying radii, Sloan, Wendland and LeGia have shown how a multiscale analysis can be applied to the approximation of Sobolev functions on a bounded domain and on the unit sphere. Here, we examine the application of this analysis to the solution of linear moderately ill-posed problems using Support Vector Approach regularization. Motivated by existing CSRBF-based multiscale regression methods, the multiscale reconstruction for an ill-posed problem is constructed by a sequence of residual corrections, where different support radii are employed to accommodate different scales. Convergence proof for the case of noise-free data and noisy data are derived from an appropriate choice of the Vapnik’s cut-off parameter and the regularization parameter. Numerical examples are constructed to verify the efficiency of the proposed approach and the effectiveness of the parameter choices.
Southeast University, Nanjing, PR China
Tue, 15/08/2017 - 11:05am
CLB-1, Central Lecture Block, UNSW