Dynamical systems gradient method for solving ill-conditioned linear algebraic systems

Details Dynamical systems gradient method for solving ill-conditioned linear algebraic systems Dynamical systems gradient method for solving ill-conditioned linear algebraic systems

2008-02-26

arxiv.org/abs/0802.3933v3

Mathematics

Numerical Analysis

1 tables, 4 figures

Scientific paper

A version of the Dynamical Systems Method (DSM) for solving ill-conditioned linear algebraic systems is studied in this paper. An {\it a priori} and {\it a posteriori} stopping rules are justified. An algorithm for computing the solution using a spectral decomposition of the left-hand side matrix is proposed. Numerical results show that when a spectral decompositon of the left-hand side matrix is available or not computationally expensive to obtain the new method can be considered as an alternative to the Variational Regularization.

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