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Volume 10, Issue 3
On the Numerical Method of Following Homotopy Paths

Feng-Guang Zhao & De-Ren Wang

J. Comp. Math., 10 (1992), pp. 245-253.

Published online: 1992-10

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  • Abstract

In this paper, we develop one kind of method, called self-adaptive method (SAM), to trace a continuous curve of a homotopy system for the solution of a nonlinear system of equations in finite steps. The existence of the continuous solution, the determination of safe initial points, and the test of regularity and stop criterion corresponding to this method are discussed. As a result, the method can follow the curve efficiently. The numerical results show that our method is satisfactory.

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@Article{JCM-10-245, author = {Zhao , Feng-Guang and Wang , De-Ren}, title = {On the Numerical Method of Following Homotopy Paths}, journal = {Journal of Computational Mathematics}, year = {1992}, volume = {10}, number = {3}, pages = {245--253}, abstract = {

In this paper, we develop one kind of method, called self-adaptive method (SAM), to trace a continuous curve of a homotopy system for the solution of a nonlinear system of equations in finite steps. The existence of the continuous solution, the determination of safe initial points, and the test of regularity and stop criterion corresponding to this method are discussed. As a result, the method can follow the curve efficiently. The numerical results show that our method is satisfactory.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9357.html} }
TY - JOUR T1 - On the Numerical Method of Following Homotopy Paths AU - Zhao , Feng-Guang AU - Wang , De-Ren JO - Journal of Computational Mathematics VL - 3 SP - 245 EP - 253 PY - 1992 DA - 1992/10 SN - 10 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9357.html KW - AB -

In this paper, we develop one kind of method, called self-adaptive method (SAM), to trace a continuous curve of a homotopy system for the solution of a nonlinear system of equations in finite steps. The existence of the continuous solution, the determination of safe initial points, and the test of regularity and stop criterion corresponding to this method are discussed. As a result, the method can follow the curve efficiently. The numerical results show that our method is satisfactory.

Zhao , Feng-Guang and Wang , De-Ren. (1992). On the Numerical Method of Following Homotopy Paths. Journal of Computational Mathematics. 10 (3). 245-253. doi:
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