Bounding the spectrum of large Hermitian matrices

DOI10.1016/j.laa.2010.06.034zbMath1221.15022OpenAlexW2146295302MaRDI QIDQ541913

Ren-Cang Li, Yunkai Zhou

Publication date: 8 June 2011

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2010.06.034

zbMATH Keywords

algorithmupper boundlargest eigenvalueHermitian matrixLanczos iteration

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Eigenvalues, singular values, and eigenvectors (15A18) Hermitian, skew-Hermitian, and related matrices (15B57)

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Uses Software

• SparseMatrix
• mftoolbox

Cites Work

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• Self-consistent-field calculations using Chebyshev-filtered subspace iteration
• A sharp version of Kahan's theorem on clustered eigenvalues
• Matrix Algorithms
• A Chebyshev–Davidson Algorithm for Large Symmetric Eigenproblems
• Estimating the Largest Eigenvalue of a Positive Definite Matrix
• On the Rates of Convergence of the Lanczos and the Block-Lanczos Methods
• On Estimating the Largest Eigenvalue with the Lanczos Algorithm
• Estimating the Largest Eigenvalue by the Power and Lanczos Algorithms with a Random Start
• Functions of Matrices
• Estimates for Some Computational Techniques in Linear Algebra