Cheng-Yu Ku, Chein-Shan Liu, Weichung Yeih, Chia-Ming Fan
The International Conference on Computational & Experimental Engineering and Sciences, Vol.19, No.2, pp. 33-34, 2011, DOI:10.3970/icces.2011.019.033
Abstract In this paper, a novel method, named the perturbed dynamical method, is proposed to solve nonlinear systems whose Jacobian matrix is singular. The concept of the proposed method roots from the conventional homotopy method but it takes the advantages of converting a vector function to a scalar function by using the square norm of the vector function to conduct a scalar-based homotopy method. Then, a small parameter, which is similar to the perturbation theory, is introduced to the singular systems of nonlinear equations such that the modified singular systems of nonlinear equations become nonsingular and the asymptotic solutions may be… More >