Milan Hladík and Jaroslav Horáček. A shaving method for interval linear systems of equations. In Roman Wyrzykowski, Jack Dongarra, Konrad Karczewski, and Jerzy Waśniewski, editors, Parallel Processing and Applied Mathematics, LNCS, pp. 573–581, Springer, 2014.
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We propose an iterative improvement method for an enclosure of the solution set of a system of interval linear equations. The method sequentially cuts off (shaves) parts of a given enclosure that contain no solution, yielding thus tighter enclosures. Since shaving can be done independently in the coordinates, the procedure is easily parallelized. Our approach is convenient for problems with wide input intervals, where traditional methods give poor enclosures. Finally, we present a limited computational study.
@inCollection{HlaHor2014b,
author = "Milan Hlad\'{\i}k and Jaroslav Hor\'{a}{\v{c}}ek",
title = "A shaving method for interval linear systems of equations",
booktitle = "Parallel Processing and Applied Mathematics",
editor = "Wyrzykowski, Roman and Dongarra, Jack and Karczewski, Konrad and Wa\'{s}niewski, Jerzy",
publisher = "Springer",
volume = "8385",
series = "LNCS",
fseries = "Lecture Notes in Computer Science",
pages = "573-581",
year = "2014",
doi = "10.1007/978-3-642-55195-6_54",
issn = "0302-9743",
isbn = "978-3-642-55194-9",
url = "http://dx.doi.org/10.1007/978-3-642-55195-6_54",
bib2html_dl_html = "http://dx.doi.org/10.1007/978-3-642-55195-6_54",
abstract = "We propose an iterative improvement method for an enclosure of the solution set of a system of interval linear equations. The method sequentially cuts off (shaves) parts of a given enclosure that contain no solution, yielding thus tighter enclosures. Since shaving can be done independently in the coordinates, the procedure is easily parallelized. Our approach is convenient for problems with wide input intervals, where traditional methods give poor enclosures. Finally, we present a limited computational study.",
keywords = "Interval systems, interval matrix, parallelization",
}
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