Small-sample statistical condition estimation of large-scale generalized eigenvalue problems
DOI10.1016/j.cam.2015.11.022zbMath1332.65061OpenAlexW2231538522MaRDI QIDQ908367
Peter Chang-Yi Weng, Frederick Kin Hing Phoa
Publication date: 4 February 2016
Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.cam.2015.11.022
Newton's methodgeneralized eigenvalue problemSylvester equationlarge-scale problemstatistical condition estimationdeflating subspacelarge and sparse real matrix
Computational methods for sparse matrices (65F50) Point estimation (62F10) Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Matrix equations and identities (15A24) Numerical computation of matrix norms, conditioning, scaling (65F35) Conditioning of matrices (15A12)
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Solution of Lyapunov equations by alternating direction implicit iteration
- Cross-Gramian based model reduction for data-sparse systems
- Three methods for refining estimates of invariant subspaces
- Iterative solution of the Lyapunov matrix equation
- Krylov-subspace methods for the Sylvester equation
- A synopsis of Monte Carlo perturbation algorithms
- Refining estimates of invariant and deflating subspaces for large and sparse matrices and pencils
- Generalized Deflated Block-Elimination
- Stochastic Perturbation Theory
- Estimating Extremal Eigenvalues and Condition Numbers of Matrices
- Condition Estimates
- Improving the Accuracy of Computed Eigenvalues and Eigenvectors
- Expected Conditioning
- FORTRAN codes for estimating the one-norm of a real or complex matrix, with applications to condition estimation
- Mixed block elimination for linear systems with wider borders
- Error and Perturbation Bounds for Subspaces Associated with Certain Eigenvalue Problems
- On the Perturbation of Pseudo-Inverses, Projections and Linear Least Squares Problems
- Improving the Efficiency of Matrix Operations in the Numerical Solution of Stiff Ordinary Differential Equations
- An Estimate for the Condition Number of a Matrix
- Statistical Condition Estimation for Linear Least Squares
- Small-Sample Statistical Condition Estimates for General Matrix Functions
- Small-Sample Statistical Estimates for the Sensitivity of Eigenvalue Problems
- Statistical Condition Estimation for Linear Systems
- Parallel computations of eigenvalues based on a Monte Carlo approach
- Accuracy and Stability of Numerical Algorithms
- Small-Sample Statistical Estimates for Matrix Norms
- Application of ADI Iterative Methods to the Restoration of Noisy Images
- A Theory of Condition
- On the Sensitivity of the Eigenvalue Problem $Ax = \lambda Bx$
- Normal Multivariate Analysis and the Orthogonal Group
- Block Krylov subspace methods for solving large Sylvester equations
This page was built for publication: Small-sample statistical condition estimation of large-scale generalized eigenvalue problems