Volume 6, Issue 1
An Acceleration Method in the Homotopy Newton'S Continuation for Nonlinear Singular Problems
DOI:

J. Comp. Math., 6 (1988), pp. 1-6

Published online: 1988-06

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• Abstract

The nonlinear singular problem f(u)=0 is considered. Here f is a $C^3$ mapping from $E^n$ to $E^n$. The Jacobian matrix $f'(u)$ is singular at the solution u* of f(u)=0. A new acceleration method in the homotopy Newton's continuation is proposed. The quadratic convergence of the new algorithm is proved. A numerical example is given.

• Keywords

@Article{JCM-6-1, author = {}, title = {An Acceleration Method in the Homotopy Newton'S Continuation for Nonlinear Singular Problems}, journal = {Journal of Computational Mathematics}, year = {1988}, volume = {6}, number = {1}, pages = {1--6}, abstract = { The nonlinear singular problem f(u)=0 is considered. Here f is a $C^3$ mapping from $E^n$ to $E^n$. The Jacobian matrix $f'(u)$ is singular at the solution u* of f(u)=0. A new acceleration method in the homotopy Newton's continuation is proposed. The quadratic convergence of the new algorithm is proved. A numerical example is given. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9492.html} }
TY - JOUR T1 - An Acceleration Method in the Homotopy Newton'S Continuation for Nonlinear Singular Problems JO - Journal of Computational Mathematics VL - 1 SP - 1 EP - 6 PY - 1988 DA - 1988/06 SN - 6 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9492.html KW - AB - The nonlinear singular problem f(u)=0 is considered. Here f is a $C^3$ mapping from $E^n$ to $E^n$. The Jacobian matrix $f'(u)$ is singular at the solution u* of f(u)=0. A new acceleration method in the homotopy Newton's continuation is proposed. The quadratic convergence of the new algorithm is proved. A numerical example is given.