Journal
APPLIED NUMERICAL MATHEMATICS
Volume 59, Issue 12, Pages 2923-2936Publisher
ELSEVIER
DOI: 10.1016/j.apnum.2009.06.005
Keywords
System of weakly nonlinear equations; HSS iteration method; Inner/outer iteration scheme; Nonlinear iteration scheme; Local convergence
Categories
Funding
- National Basic Research Program [2005CB321702]
- National Outstanding Young Scientist Foundation [10525102]
- National Natural Science Foundation , PR China [10471146]
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Based oil separable property of the linear and the nonlinear terms and on the Hermitian and skew-Hermitian splitting of the coefficient matrix, we present the Picard-HSS and the nonlinear HSS-like iteration methods for solving a class of large scale systems of weakly nonlinear equations. The advantage of these methods over the Newton and the Newton-HSS iteration methods is that they do not require explicit construction and accurate computation of the Jacobian matrix, and only need to solve linear sub-systems of constant coefficient matrices. Hence, computational workloads and computer memory may be saved in actual implementations. Under suitable conditions, we establish local convergence theorems for both Picard-HSS and nonlinear HSS-like iteration methods. Numerical implementations show that both Picard-HSS and nonlinear HSS-like iteration methods are feasible, effective, and robust nonlinear solvers for this class of large scale systems of weakly nonlinear equations. (C) 2009 Published by Elsevier B.V. oil behalf of IMACS.
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