Directional secant method for nonlinear equations

Authors:
Heng-Bin An;Zhong-Zhi Bai
Affiliations:
State Key Laboratory of Scientific/Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematical and System Sciences, Chinese Academy ...;State Key Laboratory of Scientific/Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematical and System Sciences, Chinese Academy ...
Venue:
Journal of Computational and Applied Mathematics
Year:
2005

Citing 3
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Abstract

We present a directional secant method, a secant variant of the directional Newton method, for solving a single nonlinear equation in several variables. Under suitable assumptions, we prove the convergence and the quadratic convergence speed of this new method. Numerical examples show that the directional secant method is feasible and efficient, and has better numerical behaviour than the directional Newton method.