A geometric theory for preconditioned inverse iteration. I: Extrema of Rayleigh quotient
From MaRDI portal
Publication:1595116
DOI10.1016/S0024-3795(00)00239-1zbMath0976.65034MaRDI QIDQ1595116
Publication date: 13 May 2001
Published in: Linear Algebra and its Applications (Search for Journal in Brave)
convergenceeigenvaluespreconditioningfinite elementmultigridsymmetric eigenvalue problemlarge sparse matricespreconditioned inverse iterationRayleigh-quotient
Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Boundary value problems for second-order elliptic equations (35J25) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)
Related Items
A geometric theory for preconditioned inverse iteration IV: On the fastest convergence cases, Cluster robustness of preconditioned gradient subspace iteration eigensolvers, Preconditioned iterative methods for a class of nonlinear eigenvalue problems, Convergence Analysis of Restarted Krylov Subspace Eigensolvers, Combination of Jacobi–Davidson and conjugate gradients for the partial symmetric eigenproblem, Convergence of inexact inverse iteration with application to preconditioned iterative solvers, A new justification of the Jacobi-Davidson method for large eigenproblems, An indefinite variant of LOBPCG for definite matrix pencils, Multilevel approach for brick masonry walls. III: A strategy for free vibration analysis, The preconditioned inverse iteration for hierarchical matrices, A geometric theory for preconditioned inverse iteration applied to a subspace, On preconditioned eigensolvers and invert-Lanczos processes, Preconditioned Lanczos method for generalized Toeplitz eigenvalue problems, Preconditioned gradient iterations for the eigenproblem of definite matrix pairs, Smoothed-adaptive perturbed inverse iteration for elliptic eigenvalue problems, Towards solving large-scale topology optimization problems with buckling constraints at the cost of linear analyses, Increasing efficiency of inverse iteration, A block inverse-free preconditioned Krylov subspace method for symmetric generalized eigenvalue problems, Approximation of positive semidefinite nonlinear eigenvalue problems, A geometric theory for preconditioned inverse iteration. III: A short and sharp convergence estimate for generalized eigenvalue problems
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A subspace preconditioning algorithm for eigenvector/eigenvalue computation
- On exact estimates of the convergence rate of the steepest ascent method in the symmetric eigenvalue problem
- Iteration methods in eigenvalue problems
- A new look at the Lanczos algorithm for solving symmetric systems of linear equations
- Minimization of the computational labor in determining the first eigenvalues of differential operators
- Simultaneous Rayleigh-quotient minimization methods for Ax=lambdaBx
- Some convergence results on the method of gradients for \(Ax=\lambda Bx\)
- Simultaneous iteration for the matrix eigenvalue problem
- Preconditioning eigensolvers -- an Oxymoron?
- New iterative methods for solution of the eigenproblem
- A gradient method for the matrix eigenvalue problem \(Ax = \lambda Bx\)
- A general approach to one-step iterative methods with application to eigenvalue problems
- A geometric theory for preconditioned inverse iteration applied to a subspace
- The rate of convergence of the method of steepest descent in a Euclidean norm
- A New Class of Iterative Methods for Nonselfadjoint or Indefinite Problems
- Iterative Methods by Space Decomposition and Subspace Correction
- On the convergence of the modified method of steepest descent in the calculation of eigenvalues
- Computing an Eigenvector with Inverse Iteration
- CONJUGATE GRADIENT METHODS FOR SOLVING THE SMALLEST EIGENPAIR OF LARGE SYMMETRIC EIGENVALUE PROBLEMS
- On the Multi-Level Splitting of Finite Element Spaces for Indefinite Elliptic Boundary Value Problems
- A Jacobi–Davidson Iteration Method for Linear Eigenvalue Problems
- The site of termination of afferent fibres in the caudate nucleus