Performance and energy consumption of the SIMD Gram-Schmidt process for vector orthogonalization

被引：2

作者：

Jakobs, Thomas ^{[1
]}

Naumann, Billy ^{[1
]}

Ruenger, Gudula ^{[1
]}

机构：

[1] Tech Univ Chemnitz, Fac Comp Sci, Chemnitz, Germany

来源：

JOURNAL OF SUPERCOMPUTING | 2020年 / 76卷 / 03期

关键词：

SIMD; AVX; Linear algebra; Gram-Schmidt method; Energy consumption; Frequency scaling;

D O I：

10.1007/s11227-019-02839-0

中图分类号：

TP3 [计算技术、计算机技术];

学科分类号：

0812 ;

摘要：

In linear algebra and numerical computing, the orthogonalization of a set of vectors is an important submethod. Thus, the efficient implementation on recent architectures is required to provide a useful kernel for high-performance applications. In this article, we consider the process of orthogonalizing a set of vectors with the Gram-Schmidt method and develop SIMD implementations for processors providing the Advanced Vector Extensions (AVX), which is a set of instructions for SIMD execution on recent Intel and AMD CPUs. Several SIMD implementations of the Gram-Schmidt process for vector orthogonalization are built, and their behavior with respect to performance and energy is investigated. Especially, different ways to implement the SIMD programs are proposed and several optimizations have been studied. As hardware platforms, the Intel Core, Xeon and Xeon Phi processors with the AVX versions AVX, AVX2 and AVX512 have been used.

引用

页码：1999 / 2021

页数：23

共 50 条

[21] A SPECTRAL ITERATIVE TECHNIQUE WITH GRAM-SCHMIDT ORTHOGONALIZATION
VANDENBERG, PM
GHIJSEN, WJ
[J]. IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, 1988, 36 (04) : 769 - 772
[22] UNITARY OPERATORS, ENTANGLEMENT, AND GRAM-SCHMIDT ORTHOGONALIZATION
Hardy, Yorick
Steeb, Willi-Hans
[J]. INTERNATIONAL JOURNAL OF MODERN PHYSICS C, 2009, 20 (06): : 891 - 899
[23] PARALLEL GRAM-SCHMIDT ORTHOGONALIZATION ON A NETWORK OF TRANSPUTERS
WARING, LC
CLINT, M
[J]. PARALLEL COMPUTING, 1991, 17 (09) : 1043 - 1050
[24] Gram-Schmidt orthogonalization of equine ECG signals
Holcík, J
Hanák, J
Václavík, V
Jahn, P
Sedlinská, M
[J]. PROCEEDINGS OF THE 22ND ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY, VOLS 1-4, 2000, 22 : 908 - 911
[25] An approach of orthogonalization within the Gram-Schmidt algorithm
Rivaz, A.
Moghadam, M. Mohseni
Sadeghi, D.
Kermani, H. Momenaee
[J]. COMPUTATIONAL & APPLIED MATHEMATICS, 2018, 37 (02): : 1250 - 1262
[26] Performance evaluation of parallel Gram-Schmidt re-orthogonalization methods
Katagiri, T
[J]. HIGH PERFORMANCE COMPUTING FOR COMPUTATIONAL SCIENCE - VECPAR 2002, 2003, 2565 : 302 - 314
[27] MODIFIED GRAM-SCHMIDT PROCESS VS CLASSICAL GRAM-SCHMIDT
LONGLEY, JW
[J]. COMMUNICATIONS IN STATISTICS PART B-SIMULATION AND COMPUTATION, 1981, 10 (05): : 517 - 527
[28] Multiple description quantization via Gram-Schmidt orthogonalization
Chen, Jun
Tian, Chao
Berger, Toby
Hemami, Sheila S.
[J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 2006, 52 (12) : 5197 - 5217
[29] As Good as GOLD: Gram-Schmidt Orthogonalization by Another Name
Hunter, Michael D.
[J]. PSYCHOMETRIKA, 2016, 81 (04) : 969 - 991
[30] Distributed Gram-Schmidt Orthogonalization based on Dynamic Consensus
Sluciak, Ondrej
Strakova, Hana
Rupp, Markus
Gansterer, Wilfried N.
[J]. 2012 CONFERENCE RECORD OF THE FORTY SIXTH ASILOMAR CONFERENCE ON SIGNALS, SYSTEMS AND COMPUTERS (ASILOMAR), 2012, : 1207 - 1211

← 1 2 3 4 5 →