Error Analysis of the Cholesky QR-Based Block Orthogonalization Process for the One-Sided Block Jacobi SVD Algorithm
نویسندگان
چکیده
منابع مشابه
Parallel One - Sided Block - Jacobi Svd Algorithm
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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This technical report is devoted to the description of implementation details of the accelerated parallel one-sided block Jacobi SVD algorithm, whose analysis and design was described in [21]. We provide discuss a suitable data layout for a parallel implementation of the algorithm on a parallel computer with distributed memory. This discussion is complicated by the fact that different computati...
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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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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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The computation of a singular value decomposition of an m× n matrix A is certainly one of the most often demanded tasks in various applications. There are many algorithms for computing the full or partial singular value decomposition. Among them, the one-sided Jacobi method (coupled with some orderings) is reputable for its ability to compute the singular values as well as left and right singul...
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ژورنال
عنوان ژورنال: Computing and Informatics
سال: 2020
ISSN: 2585-8807
DOI: 10.31577/cai_2020_6_1203