Abstract
The Block Jacobi preconditioning technique based on Block Broyden method is introduced to solve nonlinear equations. This paper theoretically analyzes the time complexity of this algorithm as well as the unpreconditioned one. Numerical experiments are used to show that Block Jacobi preconditioning method, compared with the unpreconditioned one, has faster solving speed and better performance under different dimensions and numbers of blocks.
This work was supported in part by the Natural Science Foundation of Jiangsu Province under Grant No 05KJD520144 and the Foundation of the QingLan Project (KZ0040704006).
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Yang, G., Dutto, L., Fortin, M.: Inexact block Jacobi Broyden methods for solving nonlinear systems of equations. SIAM J on Scientific Computing, 1367–1392 (1997)
Geng, Y.: Analysis of parallel algorithms for solving nonlinear systems of equations. Chinese Journal of Computer, 555–777 (2000) (in Chinese)
Benzi, M.: Preconditioning Techniques for Large Linear Systems: A Survey. J. Comput. Phys., 418–477 (2002)
Jiang, P., Yang, G.: Performance Analysis of Preconditioners based on Broyden Method. Applied Mathematics and Computation (accepted for publication)
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© 2006 Springer-Verlag Berlin Heidelberg
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Jiang, P., Yang, G., Rong, C. (2006). Performance Analysis of Block Jacobi Preconditioning Technique Based on Block Broyden Method. In: Alexandrov, V.N., van Albada, G.D., Sloot, P.M.A., Dongarra, J. (eds) Computational Science – ICCS 2006. ICCS 2006. Lecture Notes in Computer Science, vol 3991. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11758501_107
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DOI: https://doi.org/10.1007/11758501_107
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34379-0
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