- 期刊
MULTIPARAMETER EXTRAPOLATION AND DEFLATION METHODS FOR SOLVING EQUATION SYSTEMS
並列摘要
Most models in economics and the applied sciences are solved by first order iterative techniques, usually those based on the Gauss-Seidel algortthm, 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.
延伸閱讀
- IBRAHIM, A. (1998). FUNCTIONAL EVOLUTION EQUATIONS WITH NONCONVEX LOWER SEMICONTINUOUS MULTIVALUED PERTURBATIONS. International Journal of Mathematics and Mathematical Sciences, 1998(), 165-170. https://doi.org/10.1155/S0161171298000222
- Ceng, Q. X. (2011). A Continuation Method for Solution of Functional Differential Equation [master's thesis, Tamkang University]. Airiti Library. https://doi.org/10.6846/TKU.2011.00950
- Luo, Z. (2014). Multiple Positive Periodic Solutions for Functional Differential Equations with Impulses and a Parameter. Abstract and Applied Analysis, 2014(), 830-842-1386. https://doi.org/10.1155/2014/812867
- Akgül, A., & Kiliçman, A. (2015). Solving Delay Differential Equations by an Accurate Method with Interpolation. Abstract and Applied Analysis, (2015), 1701-1707. https://doi.org/10.1155/2015/676939
- Hemeda, A. A. (2014). Modified Homotopy Perturbation Method for Solving Fractional Differential Equations. Journal of Applied Mathematics, 2014(), 559-567-558. https://doi.org/10.1155/2014/594245