Divide and Conquer Low-Rank Preconditioners for Symmetric Matrices

• DOI: 10.1137/120872735
• Publication Date: 2013-08-13T16:36:17Z
• Authors: Ruipeng Li; Yousef Saad
• Keywords: Krylov subspace; Rank (graph theory); Low-rank approximation; Matrix (chemical analysis)

This paper presents a preconditioning method based on an approximate inverse of the original matrix, computed recursively from multilevel low-rank (MLR) expansion approach. The basic idea is to divide problem in two and apply approximation matrix obtained Sherman--Morrison formula. by few steps Lanczos bidiagonalization procedure. MLR preconditioner has been motivated its potential for exploiting different levels parallelism modern high-performance platforms, though this feature not yet tested paper. Numerical experiments indicate that, when combined with Krylov subspace accelerators, can be efficient robust solving symmetric sparse linear systems.