A parallel implementation of the Durand-Kerner algorithm for polynomial root-finding on GPU

被引：4

作者：

Ghidouche, Kahina ^{[1
]}

Couturier, Raphael ^{[2
]}

Sider, Abderrahmane ^{[1
]}

机构：

[1] Univ A Mira Bejaia, LIMED Lab, Bejaia, Algeria

[2] Univ Franche Comte, FEMTO ST Inst, IUT Belfort Montbeliard, F-90016 Belfort, France

来源：

2014 International Conference on Advanced Networking Distributed Systems and Applications (INDS 2014) | 2014年

关键词：

polynomial root-finding; high degree; iterative methods; Durant-Kerner method; GPU; CUDA; Parallelization;

D O I：

10.1109/INDS.2014.17

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

In this article we present a parallel implementation of the Durand-Kerner algorithm to find roots of polynomials of high degree on a GPU architecture (Graphics Processing Unit). We have implemented both a CPU version in C and a GPU compatible version with CUDA. The main result of our work is a parallel implementation that is 10 times as fast as its sequential counterpart on a single CPU for high degree polynomials that is greater than about 48,000.

引用

页码：53 / 57

页数：5

共 50 条

[1] Inverse power and Durand-Kerner iterations for univariate polynomial root-finding
Bini, DA
Gemignani, L
Pan, VY
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2004, 47 (2-3) : 447 - 459
[2] The globalization of Durand-Kerner algorithm
Deren W.
Fengguang Z.
Applied Mathematics and Mechanics, 1997, 18 (11) : 1045 - 1057
[3] The globalization of Durand-Kerner algorithm
Wang, DR
Zhao, FG
APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION, 1997, 18 (11) : 1045 - 1057
[4] THE GLOBALIZATION OF DURAND-KERNER ALGORITHM
赵风光
王德人
Applied Mathematics and Mechanics(English Edition), 1997, (11) : 0 - 0
[5] ON CONVERGENCE OF DURAND-KERNER METHOD FOR FINDING ALL ROOTS OF POLYNOMIAL SIMULTANEOUSLY
ZHENG, SM
KEXUE TONGBAO, 1982, 27 (12): : 1262 - 1265
[6] The convergence of Durand-Kerner method for simultaneously finding all zeros of the polynomial
Han, DF
JOURNAL OF COMPUTATIONAL MATHEMATICS, 2000, 18 (06) : 567 - 570
[7] THE CONVERGENCE OF DURAND-KERNER METHOD FOR SIMULTANEOUSLY FINDING ALL ZEROS OF THE POLYNOMIAL
Dan-fu Han (Department of Mathematics
JournalofComputationalMathematics, 2000, (06) : 567 - 570
[8] ON THE DETERMINATION OF THE SAFE INITIAL APPROXIMATION FOR THE DURAND-KERNER ALGORITHM
WANG, DR
ZHAO, FG
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1991, 38 (1-3) : 447 - 456
[9] A parallel root-finding algorithm
Nijmeijer, M. J. P.
LMS JOURNAL OF COMPUTATION AND MATHEMATICS, 2015, 18 (01): : 713 - 729
[10] SOME PARALLEL METHODS FOR POLYNOMIAL ROOT-FINDING
MAEDER, AJ
WYNTON, SA
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1987, 18 (01) : 71 - 81

← 1 2 3 4 5 →