Low-rank updates of balanced incomplete factorization preconditioners

[EN] Let Ax = b be a large and sparse system of linear equations where A is a nonsingular matrix. An approximate solution is frequently obtained by applying preconditioned terations. Consider the matrix B = A + PQT where P,Q ∈ Rn×k are full rank matrices. In this work, we study the pro...

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Bibliographic Details
Authors: Cerdán Soriano, Juana Mercedes, Marín Mateos-Aparicio, José|||0000-0002-7825-2836, Mas Marí, José|||0000-0002-2835-974X
Format: article
Publication Date:2017
Country:España
Institution:Universitat Politècnica de València (UPV)
Repository:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Language:English
OAI Identifier:oai:riunet.upv.es:10251/107359
Online Access:https://riunet.upv.es/handle/10251/107359
Access Level:Open access
Keyword:Iterative methods
Preconditioning
Low rank update
Balanced incomplete factorization
Sparse linear systems
MATEMATICA APLICADA
Description
Summary:[EN] Let Ax = b be a large and sparse system of linear equations where A is a nonsingular matrix. An approximate solution is frequently obtained by applying preconditioned terations. Consider the matrix B = A + PQT where P,Q ∈ Rn×k are full rank matrices. In this work, we study the problem of updating a previously computed preconditioner for A in order to solve the updated linear system Bx = b by preconditioned iterations. In particular, we propose a method for updating a Balanced Incomplete Factorization preconditioner. The strategy is based on the computation of an approximate Inverse Sherman-Morrison decomposition for an equivalent augmented linear system. Approximation properties of the preconditioned matrix and an analysis of the computational cost of the algorithm are studied. Moreover the results of the numerical experiments with different types of problems show that the proposed method contributes to accelerate the convergence.