ON SMOOTH LU DECOMPOSITIONS WITH APPLICATIONS TO SOLUTIONS OF NONLINEAR EIGENVALUE PROBLEMS
查看参考文献43篇
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文摘
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We study the smooth LU decomposition of a given analytic functional A-matrix A(A) and its block-analogue. Sufficient conditions for the existence of such matrix decompositions are given, some differentiability about certain elements arising from them are proved, and several explicit expressions for derivatives of the specified elements are provided. By using these smooth LU decompositions, we propose two numerical methods for computing multiple nonlinear eigenvalues of A(A), and establish their locally quadratic convergence properties. Several numerical examples are provided to show the feasibility and effectiveness of these new methods. Mathematics subject classification: 15A18, 15A23, 65F15 |
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来源
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Journal of Computational Mathematics
,2010,28(6):745-766 【核心库】
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DOI
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10.4208/jcm.1004-m0009
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关键词
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Matrix-valued function
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Smooth LU decomposition
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Pivoting
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Nonlinear eigenvalue problem
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Multiple eigenvalue
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Newton method
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地址
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1.
Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016
2.
LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190
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语种
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英文 |
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文献类型
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研究性论文 |
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ISSN
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0254-9409 |
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学科
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数学 |
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基金
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国家973计划
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国家自然科学基金国家杰出青年科学基金
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国家自然科学基金
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文献收藏号
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CSCD:4044167
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43
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