文章基本信息

标题：Multiparameter extrapolation and deflation methods for solving equation systems
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作者：A. J. Hughes Hallett
期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：1984
卷号：7
DOI：10.1155/S0161171284000818
出版社：Hindawi Publishing Corporation
摘要：Most models in economics and the applied sciences are solved by first order iterative techniques, usually those based on the Gauss-Seidel algorithm. This paper examines the convergence of multiparameter extrapolations (accelerations) of first order iterations, as an improved approximation to the Newton method for solving arbitrary nonlinear equation systems. It generalises my earlier results on single parameter extrapolations. Richardson's generalised method and the deflation method for detecting successive solutions in nonlinear equation systems are also presented as multiparameter extrapolations of first order iterations. New convergence results are obtained for those methods.