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Extended Kaczmarz‐like methods with oblique projections
Author(s) -
Popa C.
Publication year - 2003
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200310228
Subject(s) - multigrid method , oblique case , algebraic number , scalar (mathematics) , convergence (economics) , matrix (chemical analysis) , mathematics , algorithm , positive definite matrix , computer science , mathematical optimization , algebra over a field , pure mathematics , mathematical analysis , geometry , physics , partial differential equation , philosophy , linguistics , materials science , eigenvalues and eigenvectors , quantum mechanics , economics , composite material , economic growth
Abstract In this paper we describe two “sparse preconditioning” techniques for accelerating the convergence of Kaczmarzlike algorithms. The first method, uses projections with respect to the “energy scalar product” generated by an appropriate symmetric and positive definite matrix. The second one starts from some recent results of Y. Censor and T. Elfving on “sparsity pattern oriented” (SPO) oblique projections and uses an “algebraic multigrid interpolationlike” construction of the (SPO) family. Numerical experiments are described on a system comming from a bioelectric field simulation problem.