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Sigmoid-like functions and root finding methods
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DOI：10.1016/j.amc.2008.07.017.png)
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摘要
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An efficient method for finding an initial approximation to a real root of nonlinear equation f(x) = 0 is proposed. The presented approach is based on numerical integration of the transform functions tanh m(f(x)), arctan m(f(x)) (m > 0) and sgn (f(x)) of sigmoidal type. Combining numerical integration method and rapidly convergent iterative methods, we construct a hybrid method of great efficiency. The introduced sigmoid-like functions are also convenient for the detection of a cluster of zeros or a multiple zero lying in a given interval. The presented numerical examples demonstrate the feasibility and efficiency of the proposed procedures. (C) 2008 Elsevier Inc. All rights reserved.
Keyword:
Nonlinear equations
Sigmoid functions
Initial approximations
Root solvers
Numerical integration
Hybrid methods
Cluster of zeros
期刊
IF:
3.4
论文数:
2.3W
被引数:
3.3W
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