Weichung Yeih^{1,2}, Cheng-Yu Ku^{1,2,3}, Chein-Shan Liu^{4}, I-Yao Chan^{1,2}

*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 >