Parallelization of Gram-Schmidt algorithm on Intel Xeon Phi system

Domen Mladovan (2016) Parallelization of Gram-Schmidt algorithm on Intel Xeon Phi system. MSc thesis.

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Abstract

The Gram-Schmidt process is a classical process for orthonormalising a set of vectors in inner product space. There are many implementations of the Gram-Schmidt process - classical, modified and iterated classical Gram- Schmidt process. In the thesis we have chosen the classical Gram-Schmidt process. Parallelization of classical Gram-Schmidt process was implemented on Intel Xeon Phi coprocessor. We have implemented many different func- tions of classical Gram-Schmidt process in the C programming language with a help of OpenMP library. The results show that the best function is the one that evenly distributes work among all threads. First every thread calculates the same amount of projections, then the rest of projections are calculated sequentially, where the threads compute each projection in parallel. The implementation of the same function on the Intel Xeon Phi is up to three times faster than the same implementation on two Intel Xeon processors. The speedup factor is increasing with the size of input vectors.

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