线性互补问题的同步多分裂模系矩阵分裂迭代法的扰动分析任务书

 2021-08-20 12:08

1. 毕业设计(论文)主要目标:

主要研究结构矩阵线性互补问题解的扰动分析,即分析当系数矩阵发生扰动时线性互补问题的解将做如何变化。

2. 毕业设计(论文)主要内容:

本文结构做如下安排:

第一节:介绍求解线性互补问题的矩阵多重分裂迭代方法研究背景,研究现状以及相关预备知识,同时介绍本文的研究内容。

第二节:我们给出一些基本定义。

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3. 主要参考文献

1. Cottle RW, Pang J-S, Stone RE. The Linear Complementarity Problem. Academic Press: San Diego, 1992.2. Bai Z-Z. Modulus-based matrix splitting iteration methods for linear complementarity problems. Numerical LinearAlgebra with Applications 2010; 17:917–933.3. Leenaerts DMW, van Bokhoven WMG. Piecewise Linear Modeling and Analysis. Kluwer Academic Publishers:Dordrecht, 1998.4. Murty KG. Linear Complementarity, Linear and Nonlinear Programming. Heldermann-Verlag: Berlin, 1988.

5. Dong J-L, Jiang M-Q. A modified modulus method for symmetric positive-definite linear complementarity problems.Numerical Linear Algebra with Applications 2009; 16:129–143.6. Hadjidimos A, Tzoumas M. The principle of extrapolation and the Cayley transform. Linear Algebra and itsApplications 2008; 429:2465–2480.7. Hadjidimos A, Tzoumas M. Nonstationary extrapolated modulus algorithms for the solution of the linearcomplementarity problem. Linear Algebra and its Applications 2009; 431:197–210.8. Bai Z-Z. On the monotone convergence of the projected iteration methods for linear complementarity problem.Numerical Mathematics-A Journal of Chinese Universities (English Series) 1996; 5:228–233.9. Cryer CW. The solution of a quadratic programming problem using systematic overrelaxation. SIAM Journal onControl 1971; 9:385–392.10. Bai Z-Z, Sun J-C, Wang D-R. A unified framework for the construction of various matrix multisplitting iterativemethods for large sparse system of linear equations. Computers and Mathematics with Applications 1996; 32:51–76.

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