MULTILEVEL AUGMENTATION METHODS WITH MATRIX COMPRESSION FOR SOLVING REFORMULATED HAMMERSTEIN EQUATIONS

摘要

In this paper we supplement matrix truncation strategies with the multilevel augmentation methods for solving the reformulated Hammerstein equations. The resulting numerical solutions have nearly optimal convergence order with linear order computational complexity up to a logarithmic factor with respect to the dimension of the discretization subspace. Numerical experiments on one and two dimensional equations illustrate that our algorithm gains remarkably high efficiency without losing accuracy.