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Machine Theory

Parallel Processing and Applied Mathematics: 10th by Roman Wyrzykowski, Jack Dongarra, Konrad Karczewski, Jerzy

By Roman Wyrzykowski, Jack Dongarra, Konrad Karczewski, Jerzy Waśniewski

This two-volume-set (LNCS 8384 and 8385) constitutes the refereed lawsuits of the tenth overseas convention of Parallel Processing and utilized arithmetic, PPAM 2013, held in Warsaw, Poland, in September 2013. The 143 revised complete papers awarded in either volumes have been rigorously reviewed and chosen from a number of submissions. The papers disguise very important fields of parallel/distributed/cloud computing and utilized arithmetic, similar to numerical algorithms and parallel medical computing; parallel non-numerical algorithms; instruments and environments for parallel/distributed/cloud computing; functions of parallel computing; utilized arithmetic, evolutionary computing and metaheuristics.

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Additional resources for Parallel Processing and Applied Mathematics: 10th International Conference, PPAM 2013, Warsaw, Poland, September 8-11, 2013, Revised Selected Papers, Part I

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It is easily made parallel. Let CMO A be a m = r0 by n = r1 , with m > n, rectangular matrix. Assume that g = gcd(m, n) = 1. e, the above GCD Transpose algorithm works for all A. Note that this GCD algorithm has ri−1 = qi ri + ri+1 for i = 1, . . , k and rk = 1. The GCD Transpose algorithm starts with A = A02 of size r0 by r1 and produces submatrix A22 of size r2 by r3 with the rest of A as square submatrices. 1. partition A vertically into q1 r1 × r1 A1 and r2 × r1 A2 using Lemma 4 of [13] 2.

Gutheil et al. For ScaLAPACK and ELPA block sizes were in the beginning chosen to be 32. In private communication with Thomas Auckenthaler, one of the ELPA authors, we learned that for ELPA smaller blocks should be better and so we used a block size of 16 for ELPA [13] for the measurements of this article. Elemental had not yet been ported to JUQUEEN in the pre-production phase, thus all measurements were done with limited resources. We chose the default algorithmic block size of 128 which was seen to be optimal on BlueGene/P and on a preliminary BlueGene/Q hardware [11].

For TT, k < m. For vector transpose, k > 1 is arbitrary so q can be one. In Sect. 3 these types of matrices give good performance. A user can set the LDA of A so this condition always holds; see Sect. 2 of [10]. In Sect. 3 of [10] we discuss the case where m and n are not multiples of blocking factors mb and nb . The TT authors handle this related issue by using their Lemmas 3 and 4. We close this section by noting that the cycle structure of A can vary greatly when k > 1 versus k = 1 in the TT algorithm; we give two examples where k = 1, 2: q = 2, m = 3 and q = 1, m = 29.

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