A New Newton Method with Memory for Solving Nonlinear Equations
Keyword(s):
The Self
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A new Newton method with memory is proposed by using a variable self-accelerating parameter. Firstly, a modified Newton method without memory with invariant parameter is constructed for solving nonlinear equations. Substituting the invariant parameter of Newton method without memory by a variable self-accelerating parameter, we obtain a novel Newton method with memory. The convergence order of the new Newton method with memory is 1 + 2 . The acceleration of the convergence rate is attained without any additional function evaluations. The main innovation is that the self-accelerating parameter is constructed by a simple way. Numerical experiments show the presented method has faster convergence speed than existing methods.
2011 ◽
Vol 5
(2)
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pp. 298-317
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2014 ◽
Vol 2014
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pp. 1-6
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Keyword(s):
2019 ◽
Vol 57
(1)
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pp. 13-22
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