<p><span>Dynamic time warping (DTW) is an important metric for measuring similarity for most time series applications. The computations of DTW cost too much especially with the gigantic of sequence databases and lead to an urgent need for accelerating these computations. However, the multi-core cluster systems, which are available now, with their scalability and performance/cost ratio, meet the need for more powerful and efficient performance. This paper proposes a highly efficient parallel vectorized algorithm with high performance for computing DTW, addressed to multi-core clusters using the Intel quad-core Xeon co-processors. It deduces an efficient architecture. Implementations employ the potential of both message passing interface (MPI) and OpenMP libraries. The implementation is based on the OpenMP parallel programming technology and offloads execution mode, where part of the code sub-sequences on the processor side, which are uploaded to the co-processor for the DTW computations. The results of experiments confirm the effectiveness of the algorithm.</span></p>

The nonlinear conjugate gradient (NLCGM) methods have received attention because due to their simplicity, low memory requirements, and global convergent property, which allows them to be used directly to solve large-scale nonlinear unconstrained optimization problems. We suggested a modification to the β KMAR k formula, applied with three-term conjugate gradient method that is both simple and effective, denoted by (TTKMAR), which has a sufficient descent property (SDP) and ensures global convergence (GCP) when we use any line search. The numerical efficiency of TTKMAR was assessed using a variety of standard test functions. TTCGM has been demonstrated to be more numerically efficient than two-term CG methods. This paper also quantifies the difference between TTCGM and two-term methods of performance. As a result, we compare our new modification to an efficient two-term and TTCGM in the numerical results. Finally, we conclude that our proposed modification.

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