Subspace Acceleration for Large-Scale Parameter-Dependent Hermitian Eigenproblems

DOI10.1137/15M1017181zbMath1382.65104arXiv1504.06096OpenAlexW830450744MaRDI QIDQ2813334

Petar Sirković, Daniel Kressner

Publication date: 23 June 2016

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1504.06096

zbMATH Keywords

Hermitian matrixsuccessive constraint methodsubspace accelerationparameter-dependent eigenvalue problemquadratic residual bound

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) Perturbation theory of linear operators (47A55)

Related Items (8)

Subspace Acceleration for the Crawford Number and Related Eigenvalue Optimization Problems ⋮ Stochastic collocation method for computing eigenspaces of parameter-dependent operators ⋮ Dual natural-norm a posteriori error estimators for reduced basis approximations to parametrized linear equations ⋮ Low-Rank Matrix Iteration Using Polynomial-Filtered Subspace Extraction ⋮ Path-Following Method to Determine the Field of Values of a Matrix with High Accuracy ⋮ Fast sampling of parameterised Gaussian random fields ⋮ Time-varying matrix eigenanalyses via Zhang neural networks and look-ahead finite difference equations ⋮ Low-Rank Solution Methods for Stochastic Eigenvalue Problems

Uses Software

• rbMIT
• ARPACK
• lobpcg.m

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A natural-norm successive constraint method for inf-sup lower bounds
• Approximate methods for stochastic eigenvalue problems
• A Gershgorin-type lower bound for the smallest singular value
• Understanding and using linear programming
• Heuristic strategies for the approximation of stability factors in quadratically nonlinear parametrized PDEs
• Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations. Application to transport and continuum mechanics.
• Convexity of the joint numerical range: Topological and differential geometric viewpoints.
• An `empirical interpolation' method: Application to efficient reduced-basis discretization of partial differential equations
• A note on eigenvalues of perturbed Hermitian matrices
• Perturbation theory for linear operators.
• On eigenvalues of matrices dependent on a parameter
• A successive constraint linear optimization method for lower bounds of parametric coercivity and inf-sup stability constants
• ``Natural norm a posteriori error estimators for reduced basis approximations
• A New Matrix-Free Algorithm for the Large-Scale Trust-Region Subproblem
• Toward the Optimal Preconditioned Eigensolver: Locally Optimal Block Preconditioned Conjugate Gradient Method
• Subspace Methods for Computing the Pseudospectral Abscissa and the Stability Radius
• Sparse Tensor Approximation of Parametric Eigenvalue Problems
• Numerical Optimization of Eigenvalues of Hermitian Matrix Functions
• A Subspace Method for Large-Scale Eigenvalue Optimization
• ARPACK Users' Guide
• A PosterioriError Estimation for Reduced-Basis Approximation of Parametrized Elliptic Coercive Partial Differential Equations: “Convex Inverse” Bound Conditioners
• A Mathematical and Computational Framework for Reliable Real-Time Solution of Parametrized Partial Differential Equations
• Output bounds for reduced-basis approximations of symmetric positive definite eigenvalue problems
• A Spectral Bundle Method for Semidefinite Programming
• On Maximizing the Second Smallest Eigenvalue of a State-Dependent Graph Laplacian
• Reviving the Method of Particular Solutions
• Efficient greedy algorithms for high-dimensional parameter spaces with applications to empirical interpolation and reduced basis methods
• Minimizing Effective Resistance of a Graph
• The Rotation of Eigenvectors by a Perturbation. III

This page was built for publication: Subspace Acceleration for Large-Scale Parameter-Dependent Hermitian Eigenproblems