A Multilevel LSSVM for Elliptic Partial Differential Equations

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.