An indefinite variant of LOBPCG for definite matrix pencils
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Publication:403080
DOI10.1007/s11075-013-9754-3zbMath1297.65040OpenAlexW1971291073MaRDI QIDQ403080
Marija Miloloža Pandur, Daniel Kressner, MeiYue Shao
Publication date: 29 August 2014
Published in: Numerical Algorithms (Search for Journal in Brave)
Full work available at URL: http://infoscience.epfl.ch/record/201147
preconditioningnumerical experimentquadratic eigenvalue problemsdefinite matrix pencilgeneralized Hermitian eigenvalue problemslocally optimal block preconditioned conjugate gradient (LOBPCG) methodminimization principleproduct eigenvalue problems
Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Matrix pencils (15A22) Preconditioners for iterative methods (65F08)
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Uses Software
Cites Work
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- Damped oscillations of linear systems. A mathematical introduction
- Block-oriented \(J\)-Jacobi methods for Hermitian matrices
- Basis selection in LOBPCG
- Matrices and indefinite scalar products
- A Jacobi eigenreduction algorithm for definite matrix pairs
- Efficient solution of symmetric eigenvalue problems using multigrid preconditioners in the locally optimal block conjugate gradient method
- A geometric theory for preconditioned inverse iteration. I: Extrema of Rayleigh quotient
- A geometric theory for preconditioned inverse iteration. II: Convergence estimates
- Detecting a definite Hermitian pair and a hyperbolic or elliptic quadratic eigenvalue problem, and associated nearness problems
- Trace minimization and definiteness of symmetric pencils
- A geometric theory for preconditioned inverse iteration. III: A short and sharp convergence estimate for generalized eigenvalue problems
- Trace minimization principles for positive semi-definite pencils
- A geometric theory for preconditioned inverse iteration applied to a subspace
- Toward the Optimal Preconditioned Eigensolver: Locally Optimal Block Preconditioned Conjugate Gradient Method
- Minimization Principles for the Linear Response Eigenvalue Problem II: Computation
- Convergence Analysis of Gradient Iterations for the Symmetric Eigenvalue Problem
- NLEVP
- Variational and numerical methods for symmetric matrix pencils
- Block Locally Optimal Preconditioned Eigenvalue Xolvers (BLOPEX) in Hypre and PETSc
- Gradient Flow Approach to Geometric Convergence Analysis of Preconditioned Eigensolvers
- Quadratic Residual Bounds for the Hermitian Eigenvalue Problem
- Templates for the Solution of Algebraic Eigenvalue Problems
- Normwise Scaling of Second Order Polynomial Matrices
- On Positive Semidefinite Matrices with Known Null Space
- A Geometric Convergence Theory for the Preconditioned Steepest Descent Iteration
- Minimization Principles for the Linear Response Eigenvalue Problem I: Theory
- Preconditioned gradient iterations for the eigenproblem of definite matrix pairs
- Canonical Forms for Hermitian Matrix Pairs under Strict Equivalence and Congruence
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