High-Performance Algorithms for Numerical Linear Algebra

2019 ◽  
pp. 113-136
Author(s):  
Yusaku Yamamoto
Keyword(s):  
Linear Algebra ◽  
High Performance ◽  
Numerical Linear Algebra

A survey of power and energy efficient techniques for high performance numerical linear algebra operations

2014 ◽  
Vol 40 (10) ◽  
pp. 559-573 ◽  
Author(s):  
Li Tan ◽  
Shashank Kothapalli ◽  
Longxiang Chen ◽  
Omar Hussaini ◽  
Ryan Bissiri ◽  
...  
Keyword(s):  
Linear Algebra ◽  
Energy Efficient ◽  
High Performance ◽  
Numerical Linear Algebra ◽  
Power And Energy

Numerical Linear Algebra for High-Performance Computers

1998 ◽  
Author(s):  
Jack J. Dongarra ◽  
Iain S. Duff ◽  
Danny C. Sorensen ◽  
Henk A. van der Vorst
Keyword(s):  
Linear Algebra ◽  
High Performance ◽  
Numerical Linear Algebra ◽  
High Performance Computers

scholarly journals Ginkgo: A high performance numerical linear algebra library

2020 ◽  
Vol 5 (52) ◽  
pp. 2260
Author(s):  
Hartwig Anzt ◽  
Terry Cojean ◽  
Yen-Chen Chen ◽  
Goran Flegar ◽  
Fritz Göbel ◽  
...  
Keyword(s):  
Linear Algebra ◽  
High Performance ◽  
Numerical Linear Algebra

scholarly journals Replicated Computational Results (RCR) Report for “Adaptive Precision Block-Jacobi for High Performance Preconditioning in the Ginkgo Linear Algebra Software”

2021 ◽  
Vol 47 (2) ◽  
pp. 1-4
Author(s):  
Sarah Osborn
Keyword(s):  
Linear Algebra ◽  
High Performance ◽  
Numerical Linear Algebra ◽  
Practical Implementation ◽  
Test Problems ◽  
And Performance ◽  
Nvidia Gpu ◽  
Gpu Architectures ◽  
Performance Results ◽  
Conjugate Gradient Solver

The article by Flegar et al. titled “Adaptive Precision Block-Jacobi for High Performance Preconditioning in the Ginkgo Linear Algebra Software” presents a novel, practical implementation of an adaptive precision block-Jacobi preconditioner. Performance results using state-of-the-art GPU architectures for the block-Jacobi preconditioner generation and application demonstrate the practical usability of the method, compared to a traditional full-precision block-Jacobi preconditioner. A production-ready implementation is provided in the Ginkgo numerical linear algebra library. In this report, the Ginkgo library is reinstalled and performance results are generated to perform a comparison to the original results when using Ginkgo’s Conjugate Gradient solver with either the full or the adaptive precision block-Jacobi preconditioner for a suite of test problems on an NVIDIA GPU accelerator. After completing this process, the published results are deemed reproducible.

Adaptive Precision Block-Jacobi for High Performance Preconditioning in the Ginkgo Linear Algebra Software

2021 ◽  
Vol 47 (2) ◽  
pp. 1-28
Author(s):  
Goran Flegar ◽  
Hartwig Anzt ◽  
Terry Cojean ◽  
Enrique S. Quintana-Ortí
Keyword(s):  
Linear Algebra ◽  
Graphics Processing Units ◽  
High Performance ◽  
Numerical Algorithms ◽  
Mixed Precision ◽  
Before And After ◽  
Memory Accesses ◽  
Specialized Hardware ◽  
The Individual ◽  
Graphics Processing

The use of mixed precision in numerical algorithms is a promising strategy for accelerating scientific applications. In particular, the adoption of specialized hardware and data formats for low-precision arithmetic in high-end GPUs (graphics processing units) has motivated numerous efforts aiming at carefully reducing the working precision in order to speed up the computations. For algorithms whose performance is bound by the memory bandwidth, the idea of compressing its data before (and after) memory accesses has received considerable attention. One idea is to store an approximate operator–like a preconditioner–in lower than working precision hopefully without impacting the algorithm output. We realize the first high-performance implementation of an adaptive precision block-Jacobi preconditioner which selects the precision format used to store the preconditioner data on-the-fly, taking into account the numerical properties of the individual preconditioner blocks. We implement the adaptive block-Jacobi preconditioner as production-ready functionality in the Ginkgo linear algebra library, considering not only the precision formats that are part of the IEEE standard, but also customized formats which optimize the length of the exponent and significand to the characteristics of the preconditioner blocks. Experiments run on a state-of-the-art GPU accelerator show that our implementation offers attractive runtime savings.

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