2012 16th Panhellenic Conference on Informatics (2012)
Piraeus, Greece Greece
Oct. 5, 2012 to Oct. 7, 2012
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/PCi.2012.12
The preconditioned iterative methods are mainly categorized into implicit preconditioned methods and explicit preconditioned methods. In this manuscript we review implicit preconditioned methods, based on incomplete and approximate factorization, and explicit preconditioned methods, based on sparse approximate inverses and explicit approximate inverses. Additionally we present the modified Moore-Penrose conditions and theoretical estimates on the iteration matrix of the explicit preconditioned method, based on explicit approximate inverses. Finally, the performance of the preconditioned iterative methods is illustrated by solving characteristic 2D elliptic problem and numerical results are given. The theoretical estimates were in qualitative agreement with the numerical results.
Sparse matrices, Approximation algorithms, Least squares approximation, Vectors, Iterative methods, Linear systems, MoorePenrose conditions, Finite difference, implicit preconditioning, approximate LU factorization, Incomplete LU factorization, explicit approximate inverse algorithms, sparse approximate inverses
E. Lipitakis, G. Gravvanis and C. Filelis-Papadopoulos, "A Note on the Comparison of a Class of Preconditioned Iterative Methods," 2012 16th Panhellenic Conference on Informatics(PCI), Piraeus, Greece Greece, 2012, pp. 204-210.