speedingupthegvwalgorithmviaasubstitutingmethod

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	speedingupthegvwalgorithmviaasubstitutingmethod
	LI Ting 1; SUN Yao 1; HUANG Zhenyu 1; WANG Dingkang 3; LIN Dongdai 1
	2019
发表期刊	系统科学与复杂性学报英文版
ISSN	1009-6124
卷号	032 期号:001 页码:205
摘要	The GVW algorithm is an efficient signature-based algorithm for computing GrSbner bases. In this paper,the authors consider the implementation of the GVW algorithm by using Hnear algebra, and speed up GVW via a substituting method.As it is well known that,most of the computing time of a GrSbner basis is spent on reductions of polynomials.Thus,linear algebraic techniques,such as matrix operations,have been used extensively to speed up the implementations.Particularly,one-direction (also called signature-safe)reduction is used in signature-based algorithms,because polynomials (or rows in matrices)with larger signatures can only be reduced by polynomials (rows)with smaller signatures.The authors propose a new method to construct sparser matrices for signature-based algorithms via a substituting method.Specifically,instead of only storing the original polynomials in GVW,the authors also record many equivalent but sparser polynomials at the same time.In matrix construction,denser polynomials are substituted by sparser equivalent ones.As the matrices get sparser,they can be eliminated more efficiently.Two specifical algorithms,Block-GVW and LM-GVW,are presented,and their combination is the Sub-GVW algorithm.The correctness of the new proposed method is proved,and the experimental results demonstrate the efficiency of this new method.
语种	英语
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/39868
专题	中国科学院数学与系统科学研究院
作者单位	1.SKLOIS,Institute of Information Engineering,Chinese Academy of Sciences 2.中国科学院 3.KLMM,Academy of Mathematics and Systems Science,Chinese Academy of Sciences
推荐引用方式 GB/T 7714	LI Ting,SUN Yao,HUANG Zhenyu,et al. speedingupthegvwalgorithmviaasubstitutingmethod[J]. 系统科学与复杂性学报英文版,2019,032(001):205.
APA	LI Ting,SUN Yao,HUANG Zhenyu,WANG Dingkang,&LIN Dongdai.(2019).speedingupthegvwalgorithmviaasubstitutingmethod.系统科学与复杂性学报英文版,032(001),205.
MLA	LI Ting,et al."speedingupthegvwalgorithmviaasubstitutingmethod".系统科学与复杂性学报英文版 032.001(2019):205.