Pub Date : 2018-06-07DOI: 10.1111/j.1399-6576.1966.tb00345.x
D. Lind, B. Marcus
a, b, c Typical symbols from an alphabet 1 A Transposed matrix 39 A > 0 Positive matrix 100 A 0 Nonnegative matrix 100 A B Matrix inequality 100 A > B Strict matrix inequality 100 A≈∼B Elementary equivalence 226 A ≈ B Strong shift equivalence 227 A ∼ B Shift equivalence 235 A Alphabet 1 A k-blocks over A 2 A Full shift over A 2 AG, A(G) Adjacency matrix of graph G 35 AG Symbolic adjacency matrix 65 adjA Adjugate of A 113 B(X) Language of X 9 Bn(X) n-blocks in X 9 βN Higher block map 12 BF (A) Bowen–Franks group 248 BFp(A) Generalized Bowen–Franks group 250 Cf Companion matrix of f 373 Ck(u) Cylinder set using block u 179 χA(t) Characteristic polynomial of A 100 (∆ A ,∆ A , δ A ) Dimension triple of A 252 dφ Degree of sliding block code φ 303 d φ Minimal number of pre-image symbols 304 E(G), E Edge set of graph 33 EI Edges with initial state I 34 E Edges with terminal state J 34 e, f, g Typical edges of a graph 33 〈E〉Q Rational vector space generated by E 397 〈E〉R R-ideal generated by E 417 F Set of forbidden blocks 5 FX(w) Follower set of a word 72 FG(I) Follower set of a state 78 fλ Minimal polynomial of λ 370 fΛ Polynomial associated to list Λ 385 [[φ]] Topological full group 476 (∂Φ, Φ) Graph homomorphism 34 G Graph 33 G Transposed graph 39 G(A), GA Graph with adjacency matrix A 35 G ∼= H Graph isomorphism 34 G[N] Higher edge graph 42 G Higher power graph 45 G= (G,L) Labeled graph 64 GX Minimal presentation of sofic shift 83 G1 ×G2 Product of graphs 87
a, b, c字母1 a转置矩阵的典型符号39 a > 0正矩阵100 a 0非负矩阵100 ab矩阵不等式100 a > b严格矩阵不等式100 a≈~ b初等等价226 a≈b强移位等价227 a ~ b移位等价235 a字母1 a在a 2 a上的k块a在a 2 AG上的完全移位，(G)的邻接矩阵图G 35 AG)象征性的邻接矩阵65 adjA伴随113 B (X)语言的X 90亿X (X) N块木块9高βN块地图12 BF (A) Bowen-Franks集团248桶(A)广义Bowen-Franks集团250 Cf伴矩阵f 373 Ck (u)气缸套使用块u 179χ(t)特征多项式的100(∆,∆,δA)维度三252 dφ的滑块代码φ303 dφ最小数量的原像符号304 E (G),E组边缘图33 EI边缘与初始状态我34 E边缘和终端状态J 34 E, f, g的典型边缘图33 E < > Q理性所产生的向量空间E 397 < E > R R-ideal由E 417 f组禁止块5外汇(w)跟随者72 FG组一个词(我)跟随者组状态78 fλλ370 f的最小多项式Λ多项式相关上市Λ385[[φ]]拓扑全组476(∂Φ,Φ)图同态34克图33克转置图39克(一个),具有邻接矩阵A的GA图35 G ~ = H图同构34 G[N]高边图42 G高幂图45 G= (G,L)标记图64 GX软移的最小表示83 G1 ×G2图的积87
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We multiplied random univariate polynomials with 8192 terms. Typical problems run 5x faster with 4 cores on a Core i7 CPU.
我们用8192项乘以随机单变量多项式。在酷睿i7 CPU上使用4核时，典型问题的运行速度要快5倍。
{"title":"Parallel Performance","authors":"M. Iskandarani","doi":"10.2307/j.ctv1ddcxfs.6","DOIUrl":"https://doi.org/10.2307/j.ctv1ddcxfs.6","url":null,"abstract":"We multiplied random univariate polynomials with 8192 terms. Typical problems run 5x faster with 4 cores on a Core i7 CPU.","PeriodicalId":384023,"journal":{"name":"Scientific Parallel Computing","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116621471","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
High Performance Fortran is an informal standard for extensions to Fortran 90 to assist its implementation on parallel architectures, particularly for data-parallel computation. Among other things, it includes directives for expressing data distribution across multiple memories, and concurrent execution features. This paper provides an informal introduction to the main features of HPF.
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