A dimensionality reduction approach to modeling protein flexibility
Proceedings of the sixth annual international conference on Computational biology
Data Allocation Algorithm for Parallel Association Rule Discovery
PAKDD '01 Proceedings of the 5th Pacific-Asia Conference on Knowledge Discovery and Data Mining
Journal of Computational Physics
Sourcebook of parallel computing
Computing smallest singular triplets with implicitly restarted Lanczos bidiagonalization
Applied Numerical Mathematics - Numerical algorithms, parallelism and applications
Newton-Krylov continuation of periodic orbits for Navier-Stokes flows
Journal of Computational Physics
Restarted block-GMRES with deflation of eigenvalues
Applied Numerical Mathematics - 6th IMACS International symposium on iterative methods in scientific computing
Eigenfrequencies of fractal drums
Journal of Computational and Applied Mathematics
A sharp error estimate for the fast Gauss transform
Journal of Computational Physics
Parallel solution of large-scale eigenvalue problem for master equation in protein folding dynamics
Journal of Parallel and Distributed Computing
Restarted block-GMRES with deflation of eigenvalues
Applied Numerical Mathematics - 6th IMACS International symposium on iterative methods in scientific computing
International Journal of Computer Vision
A Very Fast Method for Clustering Big Text Datasets
Proceedings of the 2010 conference on ECAI 2010: 19th European Conference on Artificial Intelligence
Preconditioning bandgap eigenvalue problems in three-dimensional photonic crystals simulations
Journal of Computational Physics
Fast Algorithms for the Generalized Foley-Sammon Discriminant Analysis
SIAM Journal on Matrix Analysis and Applications
Further Analysis of the Arnoldi Process for Eigenvalue Problems
SIAM Journal on Numerical Analysis
ICCSA'11 Proceedings of the 2011 international conference on Computational science and its applications - Volume Part I
P3CA: private anomaly detection across ISP networks
PETS'11 Proceedings of the 11th international conference on Privacy enhancing technologies
A Krylov Method for the Delay Eigenvalue Problem
SIAM Journal on Scientific Computing
Novel Numerical Methods for Solving the Time-Space Fractional Diffusion Equation in Two Dimensions
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Computation of eigenpair partial derivatives by Rayleigh-Ritz procedure
Journal of Computational and Applied Mathematics
Computing eigenpairs of quadratic eigensystems
Mathematical and Computer Modelling: An International Journal
Clustered embedding of massive social networks
Proceedings of the 12th ACM SIGMETRICS/PERFORMANCE joint international conference on Measurement and Modeling of Computer Systems
Low-rank update of preconditioners for the inexact Newton method with SPD Jacobian
Mathematical and Computer Modelling: An International Journal
SIAM Journal on Scientific Computing
SIAM Journal on Matrix Analysis and Applications
Original Article: Simpler GMRES with deflated restarting
Mathematics and Computers in Simulation
Computational Optimization and Applications
Computers & Mathematics with Applications
Fuzzy spectral clustering by PCCA+: application to Markov state models and data classification
Advances in Data Analysis and Classification
SMI 2013: Heat diffusion kernel and distance on surface meshes and point sets
Computers and Graphics
On a self-consistent-field-like iteration for maximizing the sum of the Rayleigh quotients
Journal of Computational and Applied Mathematics
Deflation-based power iteration clustering
Applied Intelligence
Journal of Computational and Applied Mathematics
Prescribing the behavior of early terminating GMRES and Arnoldi iterations
Numerical Algorithms
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A deflation procedure is introduced that is designed to improve the convergence of an implicitly restarted Arnoldi iteration for computing a few eigenvalues of a large matrix. As the iteration progresses, the Ritz value approximations of the eigenvalues converge at different rates. A numerically stable scheme is introduced that implicitly deflates the converged approximations from the iteration. We present two forms of implicit deflation. The first, a locking operation, decouples converged Ritz values and associated vectors from the active part of the iteration. The second, a purging operation, removes unwanted but converged Ritz pairs. Convergence of the iteration is improved and a reduction in computational effort is also achieved. The deflation strategies make it possible to compute multiple or clustered eigenvalues with a single vector restart method. A block method is not required. These schemes are analyzed with respect to numerical stability, and computational results are presented.