Ondřej Král and Milan Hladík. Parallel computing of linear systems with linearly dependent intervals in MATLAB. In R. Wyrzykowski and others, editors, Parallel Processing and Applied Mathematics, LNCS, pp. 391–401, Springer, Cham, 2018.
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We implemented several known algorithms for finding an interval enclosure of the solution set of a linear system with linearly dependent interval parameters. To do that we have chosen MATLAB environment with use of INTLAB and VERSOFT libraries. Because our implementation is tested on Toeplitz and symmetric matrices, among others, there is a problem with a sparsity. We introduce straightforward format for representing such matrices, which seems to be almost as effective as the standard matrix representation but with less memory demands. Moreover, we take an advantage of Parallel Computing Toolbox to enhance the performance of implemented methods and to get more insights on how the methods stands in a scope of a tightness-performance ratio. The contribution is a time-tightness performance comparison of such methods, memory efficient representation and an exploration of explicit parallelization impact.
@inCollection{KraHla2018a,
author = "Ond\v{r}ej Kr\'{a}l and Milan Hlad\'{\i}k",
title = "Parallel computing of linear systems with linearly dependent intervals in {MATLAB}",
editor = "R. Wyrzykowski and others",
feditor = "Wyrzykowski, Roman and Dongarra, Jack and Deelman, Ewa and Karczewski, Konrad",
booktitle = "Parallel Processing and Applied Mathematics",
publisher = "Springer",
address = "Cham",
series = "LNCS",
fseries = "Lecture Notes in Computer Science",
volume = "10778",
pages = "391-401",
year = "2018",
doi = "10.1007/978-3-319-78054-2_37",
isbn = "978-3-319-78054-2",
url = "https://doi.org/10.1007/978-3-319-78054-2_37",
bib2html_dl_html = "https://link.springer.com/chapter/10.1007/978-3-319-78054-2_37",
abstract = "We implemented several known algorithms for finding an interval enclosure of the solution set of a linear system with linearly dependent interval parameters. To do that we have chosen MATLAB environment with use of INTLAB and VERSOFT libraries. Because our implementation is tested on Toeplitz and symmetric matrices, among others, there is a problem with a sparsity. We introduce straightforward format for representing such matrices, which seems to be almost as effective as the standard matrix representation but with less memory demands. Moreover, we take an advantage of Parallel Computing Toolbox to enhance the performance of implemented methods and to get more insights on how the methods stands in a scope of a tightness-performance ratio. The contribution is a time-tightness performance comparison of such methods, memory efficient representation and an exploration of explicit parallelization impact.",
keywords = "Interval system; Linear dependency; Parallelization; MATLAB; INTLAB",
}
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