Journal of Computational and Applied Mathematics
Sparse approximate inverse smoothers for geometric and algebraic multigrid
Applied Numerical Mathematics - Developments and trends in iterative methods for large systems of equations—in memoriam Rüdiger Weiss
A parallel solver for large-scale Markov chains
Applied Numerical Mathematics - Developments and trends in iterative methods for large systems of equations—in memoriam Rüdiger Weiss
New methods for adapting and for approximating inverses as preconditioners
Applied Numerical Mathematics - Developments and trends in iterative methods for large systems of equations—in memoriam Rüdiger Weiss
Generalized least-squares polynomial preconditioners for symmetric indefinite linear equations
Parallel Computing - Parallel matrix algorithms and applications
Preconditioning techniques for large linear systems: a survey
Journal of Computational Physics
Band preconditioners: application to preconditioned conjugate gradient methods on parallel computers
Parallel numerical linear algebra
ICCS '02 Proceedings of the International Conference on Computational Science-Part II
A Parallel Algebraic Preconditioner for the Schur Complement System
IPDPS '01 Proceedings of the 15th International Parallel & Distributed Processing Symposium
Parallel Subdomain-Based Preconditioner for the Schur Complement
Euro-Par '99 Proceedings of the 5th International Euro-Par Conference on Parallel Processing
Robust Preconditioning of Dense Problems from Electromagnetics
NAA '00 Revised Papers from the Second International Conference on Numerical Analysis and Its Applications
A new data-mapping scheme for latency-tolerant distributed sparse triangular solution
Proceedings of the 2002 ACM/IEEE conference on Supercomputing
Applied Numerical Mathematics
The Journal of Supercomputing
Factorized Sparse Approximate Inverses for Preconditioning
The Journal of Supercomputing
Global and localized parallel preconditioning techniques for large scale solid Earth simulations
Future Generation Computer Systems - Selected papers from CCGRID 2002
The effect of orderings on sparse approximate inverse preconditioners for non-symmetric problems
Advances in Engineering Software - Engineering computational technology
Effectiveness of approximate inverse preconditioning by using the MR algorithm on an origin 2400
ICECT'03 Proceedings of the third international conference on Engineering computational technology
Some greedy learning algorithms for sparse regression and classification with mercer kernels
The Journal of Machine Learning Research
Multilevel block ILU preconditioner for sparse nonsymmetric M-matrices
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the international conference on linear algebra and arithmetic, Rabat, Morocco, 28-31 May 2001
Fast computational methods for locating fold points for the power flow equations
Journal of Computational and Applied Mathematics - Special Issue: Proceedings of the 10th international congress on computational and applied mathematics (ICCAM-2002)
Restarted simpler GMRES augmented with harmonic Ritz vectors
Future Generation Computer Systems - Special issue: Selected numerical algorithms
BILUS: a block version of ILUS factorization
The Korean Journal of Computational & Applied Mathematics
An MPI Implementation of the SPAI Preconditioner on the T3E
International Journal of High Performance Computing Applications
International Journal of High Performance Computing Applications
International Journal of High Performance Computing Applications
Using Python for large scale linear algebra applications
Future Generation Computer Systems - Special section: Complex problem-solving environments for grid computing
Parallel and systolic solution of normalized explicit approximate inverse preconditioning
The Journal of Supercomputing - Special issue: Parallel and distributed processing and applications
Diagonally-striped matrices and approximate inverse preconditioners
Journal of Computational and Applied Mathematics
Some convergence estimates for algebraic multilevel preconditioners
Contemporary mathematics
Wavelet-based SPAI pre-conditioner using local dropping
Mathematics and Computers in Simulation - Special issue: Applied and computational mathematics - selected papers of the fifth PanAmerican workshop - June 21-25, 2004, Tegucigalpa, Honduras
Large sparse linear systems arising from mimetic discretization
Computers & Mathematics with Applications
Parallel preconditioned conjugate gradient square method based on normalized approximate inverses
Scientific Programming - International Symposium of Parallel and Distributed Computing & International Workshop on Algorithms, Models and Tools for Parallel Computing on Heterogenous Networks
Incremental spectral preconditioners for sequences of linear systems
Applied Numerical Mathematics
Journal of Computational and Applied Mathematics
A frequency-domain technique for statistical timing analysis of clock meshes
Proceedings of the 2007 IEEE/ACM international conference on Computer-aided design
International Journal of Computing Science and Mathematics
Scaling climate simulation applications on the IBM Blue Gene/L system
IBM Journal of Research and Development
International Journal of Computer Mathematics - Fast Iterative and Preconditioning Methods for Linear and Non-Linear Systems
Frobenius norm minimization and probing for preconditioning
International Journal of Computer Mathematics - Fast Iterative and Preconditioning Methods for Linear and Non-Linear Systems
Preconditioners for the conjugate gradient algorithm using Gram-Schmidt and least squares methods
International Journal of Computer Mathematics
Acceleration of Preconditioned Krylov Solvers for Bubbly Flow Problems
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part I: ICCS 2007
Parallel Approximate Finite Element Inverses on Symmetric Multiprocessor Systems
ICCS '08 Proceedings of the 8th international conference on Computational Science, Part I
An extension of the conjugate residual method to nonsymmetric linear systems
Journal of Computational and Applied Mathematics
Mathematics and Computers in Simulation
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
A splitting technique of higher order for the Navier-Stokes equations
Journal of Computational and Applied Mathematics
Cross Species Expression Analysis of Innate Immune Response
RECOMB 2'09 Proceedings of the 13th Annual International Conference on Research in Computational Molecular Biology
Stabilized approximate inverse preconditioners for indefinite matrices
Proceedings of the 46th Annual Southeast Regional Conference on XX
A two-phase preconditioning strategy of sparse approximate inverse for indefinite matrices
Computers & Mathematics with Applications
Fast vectorless power grid verification using an approximate inverse technique
Proceedings of the 46th Annual Design Automation Conference
Parallel SSOR preconditioning implemented on dynamic SMP clusters with communication on the fly
Future Generation Computer Systems
Fast multipole method applied to elastostatic BEM-FEM coupling
Computers and Structures
Using Python for large scale linear algebra applications
Future Generation Computer Systems - Special section: Complex problem-solving environments for grid computing
Diagonally-striped matrices and approximate inverse preconditioners
Journal of Computational and Applied Mathematics
Acceleration of preconditioned Krylov solvers for bubbly flow problems
PPAM'07 Proceedings of the 7th international conference on Parallel processing and applied mathematics
An efficient parallel implementation of the MSPAI preconditioner
Parallel Computing
A parallel direct solver for the simulation of large-scale power/ground networks
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
On the performance of parallel normalized explicit preconditioned conjugate gradient type methods
IPDPS'06 Proceedings of the 20th international conference on Parallel and distributed processing
Smoothing and regularization with modified sparse approximate inverses
Journal on Image and Video Processing - Special issue on iterative signal processing in communications
Journal of Computational Physics
SIAM Journal on Scientific Computing
A Block FSAI-ILU Parallel Preconditioner for Symmetric Positive Definite Linear Systems
SIAM Journal on Scientific Computing
Power grid verification using node and branch dominance
Proceedings of the 48th Design Automation Conference
On the GPGPU parallelization issues of finite element approximate inverse preconditioning
Journal of Computational and Applied Mathematics
Finite-element based sparse approximate inverses for block-factorized preconditioners
Advances in Computational Mathematics
Parallel exact and approximate arrow-type inverses on symmetric multiprocessor systems
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part I
The Journal of Supercomputing
Advances in Engineering Software
Early P/G grid voltage integrity verification
Proceedings of the International Conference on Computer-Aided Design
Parallelising matrix operations on clusters for an optimal control-based quantum compiler
Euro-Par'06 Proceedings of the 12th international conference on Parallel Processing
Parallel acceleration of krylov solvers by factorized approximate inverse preconditioners
VECPAR'04 Proceedings of the 6th international conference on High Performance Computing for Computational Science
Parallel hybrid sparse solvers through flexible incomplete cholesky preconditioning
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
Power grid analysis and verification considering temperature variations
Microelectronics Journal
Parallel preconditioned conjugate gradient algorithm on GPU
Journal of Computational and Applied Mathematics
On iterative techniques for computing flow in large two-dimensional discrete fracture networks
Journal of Computational and Applied Mathematics
Proceedings of the 2012 Symposium on High Performance Computing
Sparse approximate inverse preconditioners for iterative solvers on GPUs
Proceedings of the 2012 Symposium on High Performance Computing
Adaptive Pattern Research for Block FSAI Preconditioning
SIAM Journal on Scientific Computing
Facing the Multicore-Challenge II
Facing the Multicore-Challenge II
Overview of vectorless/early power grid verification
Proceedings of the International Conference on Computer-Aided Design
On numerical modeling performance of generalized preconditioned methods
Proceedings of the 6th Balkan Conference in Informatics
A generalized Block FSAI preconditioner for nonsymmetric linear systems
Journal of Computational and Applied Mathematics
A generalization of the optimal diagonal approximate inverse preconditioner
Computers & Mathematics with Applications
Parameter estimation in high dimensional Gaussian distributions
Statistics and Computing
| Hi-index | 0.02 |
A parallel preconditioner is presented for the solution of general sparse linear systems of equations. A sparse approximate inverse is computed explicitly and then applied as a preconditioner to an iterative method. The computation of the preconditioner is inherently parallel, and its application only requires a matrix-vector product. The sparsity pattern of the approximate inverse is not imposed a priori but captured automatically. This keeps the amount of work and the number of nonzero entries in the preconditioner to a minimum. Rigorous bounds on the clustering of the eigenvalues and the singular values are derived for the preconditioned system, and the proximity of the approximate to the true inverse is estimated. An extensive set of test problems from scientific and industrial applications provides convincing evidence of the effectiveness of this approach.