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Volume 10, Issue 3
A New Type of Reduced Dimension Path Following Methods

Shu-Gong Zhang & Guo-Chen Feng

J. Comp. Math., 10 (1992), pp. 263-272.

Published online: 1992-10

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  • Abstract

To solve $F(x)=0$ numerically, we first prove that there exists a tube-like neighborhood around the curve in $R^n$ defined by the Newton homotopy in which $F(x)$ possesses some good properties. Then in this neighborhood, we set up an algorithm which is numerically stable and convergent. Since we can ensure that the iterative points are not far from the homotopy curve while computing, we need not apply the predictor-corrector which is often used in path following methods.

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@Article{JCM-10-263, author = {Zhang , Shu-Gong and Feng , Guo-Chen}, title = {A New Type of Reduced Dimension Path Following Methods}, journal = {Journal of Computational Mathematics}, year = {1992}, volume = {10}, number = {3}, pages = {263--272}, abstract = {

To solve $F(x)=0$ numerically, we first prove that there exists a tube-like neighborhood around the curve in $R^n$ defined by the Newton homotopy in which $F(x)$ possesses some good properties. Then in this neighborhood, we set up an algorithm which is numerically stable and convergent. Since we can ensure that the iterative points are not far from the homotopy curve while computing, we need not apply the predictor-corrector which is often used in path following methods.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9359.html} }
TY - JOUR T1 - A New Type of Reduced Dimension Path Following Methods AU - Zhang , Shu-Gong AU - Feng , Guo-Chen JO - Journal of Computational Mathematics VL - 3 SP - 263 EP - 272 PY - 1992 DA - 1992/10 SN - 10 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9359.html KW - AB -

To solve $F(x)=0$ numerically, we first prove that there exists a tube-like neighborhood around the curve in $R^n$ defined by the Newton homotopy in which $F(x)$ possesses some good properties. Then in this neighborhood, we set up an algorithm which is numerically stable and convergent. Since we can ensure that the iterative points are not far from the homotopy curve while computing, we need not apply the predictor-corrector which is often used in path following methods.

Zhang , Shu-Gong and Feng , Guo-Chen. (1992). A New Type of Reduced Dimension Path Following Methods. Journal of Computational Mathematics. 10 (3). 263-272. doi:
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