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Dynamical systems gradient method for solving ill-conditioned linear algebraic systems. (English) Zbl 1236.65039

Summary: A version of the dynamical systems method for solving ill-conditioned linear algebraic systems is studied. 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 decomposition 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.

MSC:

65F22 Ill-posedness and regularization problems in numerical linear algebra
65F10 Iterative numerical methods for linear systems
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