NDLI: A parameterized multi-step Newton method for solving systems of nonlinear equations

Content Provider	Springer Nature Link
Author	Ahmad, Fayyaz Tohidi, Emran Carrasco, Juan A.
Copyright Year	2015
Abstract	We construct a novel multi-step iterative method for solving systems of nonlinear equations by introducing a parameter θ to generalize the multi-step Newton method while keeping its order of convergence and computational cost. By an appropriate selection of θ, the new method can both have faster convergence and have larger radius of convergence. The new iterative method only requires one Jacobian inversion per iteration, and therefore, can be efficiently implemented using Krylov subspace methods. The new method can be used to solve nonlinear systems of partial differential equations, such as complex generalized Zakharov systems of partial differential equations, by transforming them into systems of nonlinear equations by discretizing approaches in both spatial and temporal independent variables such as, for instance, the Chebyshev pseudo-spectral discretizing method. Quite extensive tests show that the new method can have significantly faster convergence and significantly larger radius of convergence than the multi-step Newton method.
Starting Page	631
Ending Page	653
Page Count	23
File Format	PDF
ISSN	10171398
Journal	Numerical Algorithms
Volume Number	71
Issue Number	3
e-ISSN	15729265
Language	English
Publisher	Springer US
Publisher Date	2015-06-11
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Multi-step iterative methods Multi-step Newton method Systems of nonlinear equations Partial differential equations Discretization methods for partial differential equations Numeric Computing Algorithms Algebra Theory of Computation Numerical Analysis
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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