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On eigenvalue perturbation bounds for Hermitian block tridiagonal matrices
Institution:1. School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, PR China;2. Department of Mathematics, University of Macau, Macau, PR China;3. School of Software, South China Normal University, Foshan, 528225, PR China;1. Department of Mathematics and Computer Science, Xavier University, Cincinnati, OH 45207, USA;2. Instituto Universitario de Matemática Multidiscilpinar, Universitat Politècnica de València, E-46022 Valencia, Spain;3. Department of Mathematics, Pacific Lutheran University, Tacoma, WA 98447, USA;1. Departamento de Matemáticas, Facultad de Matemáticas, Universidad de Murcia, 30100 Espinardo, Murcia, Spain;2. Instituto Universitario de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain;3. Departamento de Matemática Aplicada, Facultad de Informática, Universidad de Murcia, 30100 Espinardo, Murcia, Spain;1. Department of Mathematics, National Central University, Chung-Li 32001, Taiwan;2. Department of Applied Mathematics, National Chiao Tung University, Hsinchu 30010, Taiwan;1. Pure Mathematics Research Centre, Queen''s University Belfast, Belfast BT7 1NN, United Kingdom;2. Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, Sweden
Abstract:In this paper, we give some structured perturbation bounds for generalized saddle point matrices and Hermitian block tridiagonal matrices. Our bounds improve some existing ones. In particular, the proposed bounds reveal the sensitivity of the eigenvalues with respect to perturbations of different blocks. Numerical examples confirm the theoretical results.
Keywords:Eigenvalue perturbation  Weyl's bound  Saddle point matrices  Hermitian block tridiagonal matrices
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