Abstract
Many iterative processes can be interpreted as discrete dynamical systems and, in certain cases, they correspond to a time discretization of differential systems. In this paper, we propose to derive iterative schemes for solving linear systems of equations by modeling the problem to solve as a stable state of a proper differential system; the solution of the original linear problem is then computed numerically by applying a time marching scheme. We discuss some aspects of this approach, which allows to recover some known methods but also to introduce new ones. We give convergence results and numerical illustrations.
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Communicated by H. Sadok
AMS subject classification
65F10, 65F35, 65L05, 65L12, 65L20, 65N06
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Chehab, JP., Laminie, J. Differential equations and solution of linear systems. Numer Algor 40, 103–124 (2005). https://doi.org/10.1007/s11075-005-1523-5
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DOI: https://doi.org/10.1007/s11075-005-1523-5