A Scalar Homotopy Method with Optimal Hybrid Search Directions for Solving Nonlinear Algebraic Equations
Weichung Yeih1,2, Cheng-Yu Ku1,2,3, Chein-Shan Liu4, I-Yao Chan1,2
CMES-Computer Modeling in Engineering & Sciences, Vol.90, No.4, pp. 255-282, 2013, DOI:10.3970/cmes.2013.090.255
Abstract In this paper, a scalar homotopy method with optimal hybrid search directions for solving nonlinear algebraic equations is proposed. To conduct the proposed method, we first convert the vector residual function to a scalar function by taking the square norm of the vector function and then, introduce a fictitious time variable to form a scalar homotopy function. To improve the convergence and the accuracy of the proposed method, a vector with multiple search directions and an iterative algorithm are introduced into the evolution dynamics of the solutions. Further, for obtaining the optimal search direction, linear… More >
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