On eigenvalues of a Rayleigh quotient matrix

DOI10.1016/0024-3795(92)90181-9zbMath0761.15006OpenAlexW2069647907MaRDI QIDQ1187397

Ren-Cang Li

Publication date: 23 July 1992

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

Full work available at URL: https://doi.org/10.1016/0024-3795(92)90181-9

zbMATH Keywords

eigenvaluesiterative algorithmsHermitian matrixRayleigh quotient matrixspectral variation\(QR\) methodsimultaneous method

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)

Related Items (8)

On eigenvalue variations of Rayleigh quotient matrix pencils of a definite pencil ⋮ On extremum properties of orthogonal quotients matrices ⋮ A sharp version of Kahan's theorem on clustered eigenvalues ⋮ Rayleigh--Ritz Majorization Error Bounds of Mixed Type ⋮ Residual bounds for unitarily invariant norms on clustered eigenvalues ⋮ A structured rank-revealing method for Sylvester matrix ⋮ Sharpness in rates of convergence for the symmetric Lanczos method ⋮ Increasing efficiency of inverse iteration

Cites Work

• Relative eigenvalues of a definite matrix pair
• Relative eigenvalues of Hermitian matrices
• A new look at the Lanczos algorithm for solving symmetric systems of linear equations
• Eigenvalues of Rayleigh quotient matrices
• The variation of the spectrum of a normal matrix
• SYMMETRIC GAUGE FUNCTIONS AND UNITARILY INVARIANT NORMS
• Two Simple Residual Bounds for the Eigenvalues of a Hermitian Matrix
• On the Perturbation of Pseudo-Inverses, Projections and Linear Least Squares Problems
• An Extremum Property of Sums of Eigenvalues
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