Dynamical Systems Gradient Method for Solving Ill-Conditioned Linear Algebraic Systems

作者：Hoang N S; Ramm A G^*

来源：Acta Applicandae Mathematicae, 2010, 111(2): 189-204.

DOI：10.1007/s10440-009-9540-3

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

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 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.

• 出版日期2010-8