Performance analysis and optimization of the parallel one‐sided block Jacobi SVD algorithm with dynamic ordering and variable blocking
نویسندگان
چکیده
منابع مشابه
Parallel One-Sided Block Jacobi SVD Algorithm with Dynamic Ordering and Variable Blocking: Performance Analysis and Optimization
The one-sided block Jacobi (OSBJ) method is known to be an efficient method for computing the singular value decomposition on a parallel computer. In this paper, we focus on the most recent variant of the OSBJ method, the one with parallel dynamic ordering and variable blocking, and present both theoretical and experimental analyses of the algorithm. In the first part of the paper, we provide a...
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The serial Jacobi algorithm (either one-sided or two-sided) for the computation of a singular value decomposition (SVD) of a general matrix has excellent numerical properties and parallelization potential, but it is considered to be the slowest method for computing the SVD. Even its parallelization with some parallel cyclic (static) ordering of subproblems does not lead to much improvement when...
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We show experimentally, that the QR factorization with the complete column pivoting, optionally followed by the LQ factorization of the Rfactor, can lead to a substantial decrease of the number of outer parallel iteration steps in the parallel block-Jacobi SVD algorithm, whereby the details depend on the condition number and on the shape of spectrum, including the multiplicity of singular value...
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A new dynamic ordering is presented for the parallel one-sided block Jacobi SVD algorithm. Similarly to the two-sided variant, which has been analyzed and implemented in last 10 years, the dynamic ordering takes into account the actual status of a matrix—this time of its block columns with respect to their mutual orthogonality. Using p processors, in each parallel iteration step the p mostly in...
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We have designed, implemented and tested (by simulation on a serial computer) the new dynamic ordering for the parallel one-sided block-Jacobi SVD algorithm. Our idea is based on the estimation of the cosines of principal angles between two block columns X and Y of the same width without explicitly forming the matrix product XY (or Y X) and computing its SVD. Instead, we propose to use a fixed ...
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ژورنال
عنوان ژورنال: Concurrency and Computation: Practice and Experience
سال: 2016
ISSN: 1532-0626,1532-0634
DOI: 10.1002/cpe.4059