Variable Preconditioning of Krylov Subspace Methods for Hierarchical Matrices With Adaptive Cross Approximation

Abstract

This paper discusses Krylov subspace methods to solve a linear system whose coefficient matrix is represented by a hierarchical matrix. We propose a preconditioning technique using a part of the original hierarchical matrix to accelerate the convergence of the Krylov subspace methods. The proposed preconditioning technique is based on the assumption that the submatrices on the original hierarchical matrix are approximated using the adaptive cross approximation or variants thereof. The performance of Krylov subspace methods with the proposed preconditioning technique is examined through numerical experiments on an electrostatic field analysis.