A FAST MULTILEVEL ALGORITHM FOR INTEGRAL EQUATIONS

摘要

We show how the discretization of integral equations by composite Gauss rules can be related to approximations of integral operators that converge in the operator norm, rather than strongly converge. From this norm convergent formulation a two-level approximate inverse can be constructed whose evaluation requires no fine mesh evaluations of the integral operator. The resulting multilevel algorithm, therefore, is roughly half as costly as the Atkinson-Brakhage iteration. The algorithm is applicable to both linear and nonlinear equations. [References: 27]