一类矩阵对间分离度的估计任务书

 2021-08-19 11:08

1. 毕业设计(论文)主要目标:

本文的主要目标是对已有的相关结果进行分析总结,同时,我们将提出并研究一类矩阵对间分离度的界估计。

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2. 毕业设计(论文)主要内容:

1 引言 1.1 研究意义 1.2 国内外研究现状2 预备知识 2.1 基本定义 2.2 引理3 主要结果 定理3.14 数值例子5 总结参考文献致谢

3. 主要参考文献

[1] B.Kgstrm. A perturbation analysis of the generalized Sylvester equation (ARLB, DRLE) = (C, F) [J]. SIAMJournal on Matrix Analysis and Applications, 1994, 15(4): 1045-1060.[2] B.Kgstrm, L.Westin: Generalized Schur methods with condition estimators for solving the generalizedSylvester equation[J]. IEEE Transactions on Automatic Control, 1989, 34(4): 745-751.[3] B.Kgstrm, P. Poromaa: LAPACK-Style algorithms and software for solving the generalized Sylvester equationand estimating separation between regular matrix pairs [J]. ACM Transactions on Mathematical Software, 1996,22(1): 78-103.[4] C.H.Chen. Perturbation analysis for solutions of algebraic Riccati equations[J]. Journal of ComputationalMathematics, 1988, 6(4): 336-347.[5] G.Hewer, C.Kenney:The sensitivity of the stable Lyapunov equation[J].SIAM Journal on Control andOptimization, 1988, 26(2): 321-344.[6] G.W.Stewart: Error and perturbation bounds for subspaces associated with certain eigenvalue problems[J]. SIAMReview, 1973, 15(4): 727-764.[7] J.G.Sun:Estimation of the separation of two matrices[J].Journal of Computational Mathematics, 1984, 2:189–200.[8] J.G.Sun: Estimation of the separation of two matrices (II) [J]. Journal of Computational Mathematics, 1985, 3(1):19–26 .[9] J.G.Sun: Perturbation analysis for the generalized eigenvalue and the generalized singular value problem[J]. In:B.Kgstrm, A.Ruhe (eds.) Matrix Pencils. Lecture Notes in Mathematics, 1983, 973: 221-244.[10] J.W.Demmel, B.Kgstrm. Computing stable eigendecompositions of matrix pencils[J]. Linear Algebra and itsApplications, 1987, 88(89): 139–186.[11] S.F.Xu. Lower bound estimation for the separation of two matrices [J]. Linear Algebra and its Applications, 1997,262: 67-82.[12] S.F.Xu. Sensitivity analysis of the algebraic Riccati equation[J].Numerische Mathematik, 1996, 75(1): 121-134.[13] X.S.Chen.On estimating the separation of two regular matrix pairs[J]. Numerische Mathematik, 2015:1-25.[14] P.Van Dooren: Reducing subspaces: definitions, properties and algorithms[J]. In:B. Kgstrm, A.Ruhe (eds.)Matrix Pencils. Lecture Notes in Mathematics, 1983, 973: 58-73.[15] 徐洪国.两个矩阵分离度的界[J].复旦学报(自然科学版),1994, 33(4): 413-420.[16] J.W.Demmel, B.Kgstrm. Stable eigendecompositions of matrix pencils AλB[N]. UMINF-118.84, Instituteof Information Processing, University of Ume, S-901 87 Ume, Sweden, 1984.[17] G.W. Stewart, 孙继广. Matrix Perturbation Theory[M]. San Diego: Academic, 1990.[18] 孙继广. 矩阵扰动分析[M]. 2 版. 北京: 科学出版社, 2001.

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