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

2008/02/26 by Hoang, N. S., Ramm, A. G.
#65F10 #65F22 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.0802.3933

Abstract

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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• Solving ill-conditioned linear algebraic systems by the dynamical systems method (DSM)
• Dynamical Systems Method for solving ill-conditioned linear algebraic systems
• DSM for solving ill-conditioned linear algebraic systems
• Dynamical systems method for solving linear finite-rank operator equations
• Dynamical systems method for solving linear ill-posed problems