A Multilevel LSSVM for Elliptic Partial Differential Equations
Lin Dong *
East China University of Science and Technology, Shanghai 200237, P.R. China.
Jie Liao
East China University of Science and Technology, Shanghai 200237, P.R. China.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we propose a multilevel least square support vector machine (LSSVM) for solving elliptic boundary value problems based on wavelet kernel functions. This algorithm is constructed by a sequence of residual corrections and separating the computations of different levels, where different scale parameters are employed to accommodate different scales. In this multilevel algorithm, a coarse data set and a large scale parameter are chosen and the target function is interpolated in this data set to capture the large-scale variations of the target function at the first level, next, a smaller scale parameter is used to interpolate the residuals on a ner data set, capturing the finer details on the second level. The numerical tests on some linear second order elliptic boundary value problems show the efficiency of the multilevel algorithm.
Keywords: Wavelet kernel function, least square support vector machine, multilevel