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Volume 2, Issue 3
Several Abstract Iterative Schemes for Solving the Bifurcation at Simple Eigenvalues

Zhong-Hua Yang

J. Comp. Math., 2 (1984), pp. 201-209.

Published online: 1984-02

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  • Abstract

In this paper we consider the nonlinear operator equation $\lambda x=Lx+G(\lambda,x)$ where $L$ is a closed linear operator of $X-›X, X$ is a real Banach Space, with a simple eigenvalue $\lambda_0\neq 0$. We discretize its Liapunov-Schmidt bifurcation equation instead of the original nonlinear operator equation and estimate the approximating order of our approximate solution to the genuine solution. Our method is more convenient and more accurate. Meanwhile we put forward several abstract Newton-type iterative schemes, which are more efficient for practical computation, and get the result of their super-linear convergence.

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@Article{JCM-2-201, author = {Zhong-Hua Yang}, title = {Several Abstract Iterative Schemes for Solving the Bifurcation at Simple Eigenvalues}, journal = {Journal of Computational Mathematics}, year = {1984}, volume = {2}, number = {3}, pages = {201--209}, abstract = {

In this paper we consider the nonlinear operator equation $\lambda x=Lx+G(\lambda,x)$ where $L$ is a closed linear operator of $X-›X, X$ is a real Banach Space, with a simple eigenvalue $\lambda_0\neq 0$. We discretize its Liapunov-Schmidt bifurcation equation instead of the original nonlinear operator equation and estimate the approximating order of our approximate solution to the genuine solution. Our method is more convenient and more accurate. Meanwhile we put forward several abstract Newton-type iterative schemes, which are more efficient for practical computation, and get the result of their super-linear convergence.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9654.html} }
TY - JOUR T1 - Several Abstract Iterative Schemes for Solving the Bifurcation at Simple Eigenvalues AU - Zhong-Hua Yang JO - Journal of Computational Mathematics VL - 3 SP - 201 EP - 209 PY - 1984 DA - 1984/02 SN - 2 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9654.html KW - AB -

In this paper we consider the nonlinear operator equation $\lambda x=Lx+G(\lambda,x)$ where $L$ is a closed linear operator of $X-›X, X$ is a real Banach Space, with a simple eigenvalue $\lambda_0\neq 0$. We discretize its Liapunov-Schmidt bifurcation equation instead of the original nonlinear operator equation and estimate the approximating order of our approximate solution to the genuine solution. Our method is more convenient and more accurate. Meanwhile we put forward several abstract Newton-type iterative schemes, which are more efficient for practical computation, and get the result of their super-linear convergence.

Zhong-Hua Yang. (1984). Several Abstract Iterative Schemes for Solving the Bifurcation at Simple Eigenvalues. Journal of Computational Mathematics. 2 (3). 201-209. doi:
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