This article focuses on the optimization of PCDM, a parallel, two-dimensional (2D) Delaunay mesh generation application, and its interaction with parallel architectures based on simultaneous multithreading (SMT) processors. We first present the step-by-step effect of a series of optimizations on performance. These optimizations improve the performance of PCDM by up to a factor of six. They target issues that very often Nike Basket Blazer Mid Femme limit the performance of scientific computing codes. We then evaluate the interaction of PCDM with a real SMT-based SMP system, using both high-level metrics, such as execution time, and low-level information from hardware performance counters.
We describe new types of normal forms for braid monoids, Artin–Tits monoids, and, more Blazer Nike generally, for all monoids in which divisibility has some convenient lattice properties (“locally Garside monoids”). We show that, in the case of braids, one of these normal forms coincides with the normal form introduced by Burckel and deduce that the latter can be computed easily. This approach leads to a new, simple description for the standard order (“Dehornoy order”) of BnBn in terms of that of Bn−1Bn−1, and to a quadratic upper bound for the complexity of this order.
We describe an algorithm that first decides whether the primal-dual pair of linear programs
mincTxmaxbTys.t.Ax=bs.t.ATy⩽cx⩾0is feasible and in case it is, computes an optimal basis and optimal solutions. Here, A∈Rm×n,b∈Rm,c∈RnA∈Rm×n,b∈Rm,c∈Rn Blazer Nike Pas Cher are given. Our algorithm works with finite precision arithmetic. Yet, this precision is variable and is adjusted during the algorithm. Both the finest precision required and the complexity of the algorithm depend on the dimensions n and m as well as on the condition K(A,b,c)K(A,b,c) introduced in D. Cheung and F. Cucker [Solving linear programs with finite precision: I. Condition numbers and random programs, Math. Program. 99 (2004) 175–196].
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