Publisher DOI: 10.1007/s00791-015-0254-y
Title: H-FAINV: hierarchically factored approximate inverse preconditioners
Language: English
Authors: Kriemann, Ronald 
Le Borne, Sabine  
Keywords: Approximate factored inverse; Hierarchical matrices; Preconditioning
Issue Date: 29-Dec-2015
Source: Computing and Visualization in Science 3 (17): 135-150 (2015-06-01)
Abstract (english): 
Given a sparse matrix, its LU-factors, inverse and inverse factors typically suffer from substantial fill-in, leading to non-optimal complexities in their computation as well as their storage. In the past, several computationally efficient methods have been developed to compute approximations to these otherwise rather dense matrices. Many of these approaches are based on approximations through sparse matrices, leading to well-known ILU, sparse approximate inverse or factored sparse approximate inverse techniques and their variants. A different approximation approach is based on blockwise low rank approximations and is realized, for example, through hierarchical (š¯“—H-) matrices. While š¯“—H-inverses and š¯“—H-LU factors have been discussed in the literature, this paper will consider the construction of an approximation of the factored inverse through š¯“—H-matrices (š¯“—H-FAINV). We will describe a blockwise approach that permits to replace (exact) matrix arithmetic through approximate efficient š¯“—H-arithmetic. We conclude with numerical results in which we use approximate factored inverses as preconditioners in the iterative solution of the discretized convectionā€“diffusion problem.
ISSN: 1432-9360
Journal: Computing and visualization in science 
Institute: Mathematik E-10 
Document Type: Article
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