Restricted rank modification of the symmetric eigenvalue problem: Theoretical considerations

DOI10.1016/0024-3795(88)90309-6zbMath0652.15004OpenAlexW2021807083MaRDI QIDQ1106912

Peter Arbenz, Walter Gander, Gene H. Golub

Publication date: 1988

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

Full work available at URL: https://doi.org/10.1016/0024-3795(88)90309-6

zbMATH Keywords

eigenvalue problemsbisection methodPerturbationintermediate problems inertiarank modificationRestricted eigenvalue problemWeinstein-Aronszajn methods

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Eigenvalues, singular values, and eigenvectors (15A18)

Related Items (11)

Erratum to: Outliers in the spectrum of iid matrices with bounded rank perturbations ⋮ Outliers in the spectrum for products of independent random matrices ⋮ Solving Singular Generalized Eigenvalue Problems. Part II: Projection and Augmentation ⋮ The singular values and vectors of low rank perturbations of large rectangular random matrices ⋮ Approximate eigensolution of Laplacian matrices for locally modified graph products ⋮ Computing the eigenvalues of modified symmetric matrices ⋮ The eigenvalues and eigenvectors of finite, low rank perturbations of large random matrices ⋮ On the modification of an eigenvalue problem that preserves an eigenspace ⋮ Domain decomposition methods for eigenvalue problems ⋮ Kron's method for symmetric eigenvalue problems ⋮ Modifying the inertia of matrices arising in optimization

Uses Software

• LINPACK

Cites Work

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• Solving nonlinear eigenvalue problems by algorithmic differentiation
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• A new look at the Lanczos algorithm for solving symmetric systems of linear equations
• A Divide and Conquer method for the symmetric tridiagonal eigenproblem
• Methods of intermediate problems for eigenvalues. Theory and ramifications
• The behavior of eigenvalues and singular values under perturbations of restricted rank
• Rank-one modification of the symmetric eigenproblem
• Stationary values of the ratio of quadratic forms subject to linear constraints
• A Fully Parallel Algorithm for the Symmetric Eigenvalue Problem
• A Comparison of Algorithms for Solving Symmetric Indefinite Systems of Linear Equations
• Some Stable Methods for Calculating Inertia and Solving Symmetric Linear Systems
• Eigenproblems for Matrices Associated with Periodic Boundary Conditions
• Some Modified Matrix Eigenvalue Problems

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