On the use of harmonic Ritz pairs in approximating internal eigenpairs

DOI10.1016/S0024-3795(01)00480-3zbMath1028.65030OpenAlexW2004464554MaRDI QIDQ1855434

Jasper van den Eshof, Gerard L. G. Sleijpen

Publication date: 5 February 2003

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

Full work available at URL: https://doi.org/10.1016/s0024-3795(01)00480-3

zbMATH Keywords

algorithmserror analysiseigenvectorsreal symmetric matricesharmonic Ritz vectorblock Arnoldi processinternal eigenpairrefined Rayleigh-Ritz

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Numerical computation of eigenvalues and eigenvectors of matrices (65F15)

Related Items (6)

Convergence proof of the harmonic Ritz pairs of iterative projection methods with restart strategies for symmetric eigenvalue problems ⋮ Scalable implementation of polynomial filtering for density functional theory calculation in PARSEC ⋮ A homogeneous Rayleigh quotient with applications in gradient methods ⋮ Solving large-scale interior eigenvalue problems to investigate the vibrational properties of the boson peak regime in amorphous materials ⋮ On the subspace projected approximate matrix method. ⋮ On solving complex-symmetric eigenvalue problems arising in the design of axisymmetric VCSEL devices

Uses Software

• JDQZ

Cites Work

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• Zur Verwendung optimaler Eigenwerteingrenzungen bei der Lösung symmetrischer Matrizenaufgaben
• Optimale Eigenwerteinschließungen
• An analysis of the Rayleigh--Ritz method for approximating eigenspaces
• The Advantages of Inverted Operators in Rayleigh–Ritz Approximations
• Optimal a priori error bounds for the Rayleigh-Ritz method
• Approximate solutions and eigenvalue bounds from Krylov subspaces
• On the roots of the orthogonal polynomials and residual polynomials associated with a conjugate gradient method
• A Jacobi–Davidson Iteration Method for Linear Eigenvalue Problems
• Harmonic projection methods for large non-symmetric eigenvalue problems
• Estimates for Some Computational Techniques in Linear Algebra

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