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Abstract
In this paper, the alternating direction implicit (ADI) method is considered for solving linear systems of equations. It is shown that the rate of convergence of the ADI method can be accelerated by the successive over relaxation (SOR) method in the commutative case. Theoretical results demonstrate that the accelerated procedure, called the ADI-SOR method, results in an order of magnitude improvement. For the model problem, it is shown that the rate of convergence for the ADI-SOR scheme is asymptotically proportional to h 1/2m (where h is the mesh size and m is the number of parameters for the ADI method), while for the ADI method the rate of convergence is asymptotically proportional to h 1/m. It is also shown that the ADI-SOR method is faster than the ADI scheme with 2 m parameters.
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∗Dept. of Maths., Northeast Univ, of Tech., Shenyang, P. R. China, and Open Lab. of CAD/CAM Tech. for Advanced Manufacturing, Academia Sinica, P. R. China.
∗Dept. of Maths., Northeast Univ, of Tech., Shenyang, P. R. China, and Open Lab. of CAD/CAM Tech. for Advanced Manufacturing, Academia Sinica, P. R. China.
Notes
∗Dept. of Maths., Northeast Univ, of Tech., Shenyang, P. R. China, and Open Lab. of CAD/CAM Tech. for Advanced Manufacturing, Academia Sinica, P. R. China.