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Additive preconditioning and aggregation in matrix computations

Authors
Journal
Computers & Mathematics with Applications
0898-1221
Publisher
Elsevier
Publication Date
Volume
55
Issue
8
Identifiers
DOI: 10.1016/j.camwa.2004.03.022
Keywords
  • Matrix Computations
  • Additive Preconditioning
  • Aggregation
  • Msas
Disciplines
  • Computer Science

Abstract

Abstract We combine our novel SVD-free additive preconditioning with aggregation and other relevant techniques to facilitate the solution of a linear system of equations and other fundamental matrix computations. Our analysis and experiments show the power of our algorithms, guide us in selecting most effective policies of preconditioning and aggregation, and provide some new insights into these and related subjects. Compared to the popular SVD-based multiplicative preconditioners, our additive preconditioners are generated more readily and for a much larger class of matrices. Furthermore, they better preserve matrix structure and sparseness and have a wider range of applications (e.g., they facilitate the solution of a consistent singular linear system of equations and of the eigenproblem).

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