Selçuk Journal of Applied Mathematics

www.selcuk.edu.tr




 Selçuk Journal of
  Applied Mathematics

  Summer-Autumn, 2000
  Volume  1
  Number 1

 
Research Center of 
  Applied Mathematics


 SJAM Summer-Autumn 2000, Volume 1 - Number 1

Factorized Sparse Approximate Inverses for Preconditioning and Smoothing

Thomas Huckle 

Institut für Informatik, Technische Universität München, D-80290 München, Germany;
email: huckle@in.tum.de

Received: 25 August 2000

To Prof. Dr. Chr. Zenger 60-th birthday
 

Summary
In recent papers the use of sparse approximate inverses for the preconditioning of linear equations Ax=b is examined. The minimization of || AM-I || in the Frobenius norm generates good preconditioners without any a priori knowledge on the pattern of M. For symmetric positive definite A and a given a priori pattern there exist methods for computing factorized sparse approximate inverses L with LLT A-1. Here, we want to modify these algorithms that they are able to capture automatically a promising pattern for L. We use these approximate inverses for solving linear equations with the cg-method. Furthermore we introduce and test modifications of this method for computing factorized sparse approximate inverses that are suited for smoothing in multigrid solvers.

 

Key words
sparse linear systems, factorized sparse approximate inverses, preconditioned conjugate gradients, smoother, multi-grid
 

Mathematics Subject Classification (1991): 65F10, 65F50, 15A09, 15A23
 

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