Abstract
The purpose of paper is to analyze the behavior of the error in the iterative method. Especially, we are interested in the classical iterative method such as SOR method and its preconditioning techniques to solve the linear system \(A{u}={q}\). In order to accelerate convergence, many researchers proposed several preconditioners [4,5,6,7,8]. There is also preconditioner available for both classical iterative and Krylov subspace methods. We focus on the behavior of error to find a good preconditioner. We treat difference equation derived from partial differential equation(PDE), because the coefficient matrix given by using difference approximation is easy to investigate. By examining the behavior of the error, we choose an effective preconditioner, and show the numerical results.
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Acknowledgements
The author would like to thank the referees for pointing out some corrections. This study was supported by JSPS KAKENHI Grant Number JP 26400181.
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Kohno, T. (2017). On the Behavior of the Error in Numerical Iterative Method for PDE. In: Elaydi, S., Hamaya, Y., Matsunaga, H., Pötzsche, C. (eds) Advances in Difference Equations and Discrete Dynamical Systems. ICDEA 2016. Springer Proceedings in Mathematics & Statistics, vol 212. Springer, Singapore. https://doi.org/10.1007/978-981-10-6409-8_8
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DOI: https://doi.org/10.1007/978-981-10-6409-8_8
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