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| ON MONOTONE CONVERGENCE OF NONLINEARMULTISPLITTING RELAXATION METHODS |
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Citation： |
Wang Deren,Bai Zhongzhi.ON MONOTONE CONVERGENCE OF NONLINEARMULTISPLITTING RELAXATION METHODS[J].Chinese Annals of Mathematics B,1994,15(3):335~348 |
| Page view： 699
Net amount： 660 |
Authors： |
Wang Deren; Bai Zhongzhi |
Foundation： |
Project supported by the Natural Science
Foundation of China and Shanghai |
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| Abstract： |
A class of parallel nonlinear multisplitting
AOR methods is set up by directly multisplitting the nonlinear mapping $ F:
D\subset R^n\rightarrow R^n$ for solving the nonlinear system of equations
$ F(x)=0$. The different choices of the relaxation parameters can yield
all the known and a lot of new relaxation methods as well as a lot of
new relaxation parallel
nonlinear multisplitting methods. The two-sided approximation properties
and the influences on convergence from the relaxation parameters about
the new methods are shown, and the sufficient conditions guaranteeing the methods
to converge globally are discussed. Finally, a lot of numerical results
show that the methods are feasible and efficient. |
Keywords： |
Nonlinear system of equations, Nonlinear multisplitting,
Monotonicity,Global convergence. |
Classification： |
65H10, 65W05. |
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