Matrix analysis
A multi-level solution algorithm for steady-state Markov chains
SIGMETRICS '94 Proceedings of the 1994 ACM SIGMETRICS conference on Measurement and modeling of computer systems
Multilevel adaptive methods for elliptic eigenproblems: a two-level convergence theory
SIAM Journal on Numerical Analysis - Special issue: the articles in this issue are dedicated to Seymour V. Parter
Two-grid Method for Linear Elasticity on Unstructured Meshes
SIAM Journal on Scientific Computing
Robustness and Scalability of Algebraic Multigrid
SIAM Journal on Scientific Computing
An Aggregation Multigrid Solver for convection-diffusion problems onunstructured meshes.
An Aggregation Multigrid Solver for convection-diffusion problems onunstructured meshes.
Adaptive Smoothed Aggregation ($\alpha$SA)
SIAM Journal on Scientific Computing
Algebraic multigrid for higher-order finite elements
Journal of Computational Physics
SIAM Journal on Scientific Computing
Aggregation-Based Algebraic Multilevel Preconditioning
SIAM Journal on Matrix Analysis and Applications
Reducing Complexity in Parallel Algebraic Multigrid Preconditioners
SIAM Journal on Matrix Analysis and Applications
An Algebraic Multigrid Preconditioner for a Class of Singular M-Matrices
SIAM Journal on Scientific Computing
Analysis of Aggregation-Based Multigrid
SIAM Journal on Scientific Computing
Multilevel Adaptive Aggregation for Markov Chains, with Application to Web Ranking
SIAM Journal on Scientific Computing
Analysis of an algebraic Petrov--Galerkin smoothed aggregation multigrid method
Applied Numerical Mathematics
A New Petrov-Galerkin Smoothed Aggregation Preconditioner for Nonsymmetric Linear Systems
SIAM Journal on Scientific Computing
Towards Adaptive Smoothed Aggregation ($\alpha$SA) for Nonsymmetric Problems
SIAM Journal on Scientific Computing
Smoothed Aggregation Multigrid for Markov Chains
SIAM Journal on Scientific Computing
Algebraic Multigrid for Markov Chains
SIAM Journal on Scientific Computing
Recursively Accelerated Multilevel Aggregation for Markov Chains
SIAM Journal on Scientific Computing
Efficient Parallel AMG Methods for Approximate Solutions of Linear Systems in CFD Applications
SIAM Journal on Scientific Computing
Advances in Computational Mathematics
A Bootstrap Algebraic Multilevel Method for Markov Chains
SIAM Journal on Scientific Computing
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A new adaptive algebraic multigrid scheme is developed for the solution of Markov chains, where the hierarchy of operators is adapted on-the-fly in a setup process that is interlaced with the solution process. The setup process feeds the solution process with improved operators, while the solution process provides the adaptive setup process with better approximations on which to base further-improved operators. The approach is demonstrated using Petrov-Galerkin smoothed aggregation where only the prolongation operator is smoothed, while the restriction remains of low order. Results show that the on-the-fly adaptive scheme can improve the performance of multigrid solvers that require extensive setup computations, in both serial and parallel environments.