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

Zhong-Hua Yang

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.

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@Article{JCM-6-1, author = {Yang , Zhong-Hua}, 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 AU - Yang , Zhong-Hua 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.

Yang , Zhong-Hua. (1988). An Acceleration Method in the Homotopy Newton's Continuation for Nonlinear Singular Problems. Journal of Computational Mathematics. 6 (1). 1-6. doi:
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