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

Date

2010-07-14

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Abstract

A version of the Dynamical Systems Method (DSM) for solving ill-conditioned linear algebraic systems is studied in this paper. An a priori and 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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Keywords

Ill-conditioned linear algebraic systems, Dynamical Systems Method (DSM), Variational Regularization

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