Mixed Precision Iterative Refinement Techniques for the Solution of Dense Linear Systems

Authors:
Alfredo Buttari;Jack Dongarra;Julie Langou;Julien Langou;Piotr Luszczek;Jakub Kurzak
Affiliations:
DEPARTMENT OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE, UNIVERSITY OF TENNESSEE, KNOXVILLE, TENNESSEE;DEPARTMENT OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE, UNIVERSITY OF TENNESSEE, KNOXVILLE, TENNESSEE, OAK RIDGE NATIONAL LABORATORY, OAK RIDGE, TE ...;DEPARTMENT OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE, UNIVERSITY OF TENNESSEE, KNOXVILLE, TENNESSEE;DEPARTMENT OF MATHEMATICAL SCIENCES, UNIVERSITY OF COLORADO AT DENVER AND HEALTH SCIENCES CENTER, DENVER, COLORADO;DEPARTMENT OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE, UNIVERSITY OF TENNESSEE, KNOXVILLE, TENNESSEE;DEPARTMENT OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE, UNIVERSITY OF TENNESSEE, KNOXVILLE, TENNESSEE
Venue:
International Journal of High Performance Computing Applications
Year:
2007

Citing 7
Cited 10

Applied numerical linear algebra

Applied numerical linear algebra
Iterative Refinement in Floating Point

Journal of the ACM (JACM)
Matrix algorithms

Matrix algorithms
Accuracy and Stability of Numerical Algorithms

Accuracy and Stability of Numerical Algorithms
Rounding Errors in Algebraic Processes

Rounding Errors in Algebraic Processes
Implementation of mixed precision in solving systems of linear equations on the Cell processor: Research Articles

Concurrency and Computation: Practice & Experience
Using Mixed Precision for Sparse Matrix Computations to Enhance the Performance while Achieving 64-bit Accuracy

ACM Transactions on Mathematical Software (TOMS)

Solving Dense Linear Systems on Graphics Processors

Euro-Par '08 Proceedings of the 14th international Euro-Par conference on Parallel Processing
Low cost high performance uncertainty quantification

Proceedings of the 2nd Workshop on High Performance Computational Finance
A fast and robust mixed-precision solver for the solution of sparse symmetric linear systems

ACM Transactions on Mathematical Software (TOMS)
Scalable heterogeneous parallelism for atmospheric modeling and simulation

The Journal of Supercomputing
Towards energy efficient parallel computing on consumer electronic devices

ICT-GLOW'11 Proceedings of the First international conference on Information and communication on technology for the fight against global warming
Mixed precision iterative refinement methods for linear systems: convergence analysis based on krylov subspace methods

PARA'10 Proceedings of the 10th international conference on Applied Parallel and Scientific Computing - Volume 2
Low-cost data uncertainty quantification

Concurrency and Computation: Practice & Experience
Profiling high performance dense linear algebra algorithms on multicore architectures for power and energy efficiency

Computer Science - Research and Development
GPU-accelerated asynchronous error correction for mixed precision iterative refinement

Euro-Par'12 Proceedings of the 18th international conference on Parallel Processing
Iterative refinement techniques for solving block linear systems of equations

Applied Numerical Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

By using a combination of 32-bit and 64-bit floating point arithmetic, the performance of many dense and sparse linear algebra algorithms can be significantly enhanced while maintaining the 64-bit accuracy of the resulting solution. The approach presented here can apply not only to conventional processors but also to exotic technologies such as Field Programmable Gate Arrays (FPGA), Graphical Processing Units (GPU), and the Cell BE processor. Results on modern processor architectures and the Cell BE are presented.