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 - <p style="text-align: justify;">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.</p>