Jaroslav Horáček and Milan Hladík. Subsquares approach -- A simple scheme for solving overdetermined interval linear systems. In Roman Wyrzykowski, Jack Dongarra, Konrad Karczewski, and Jerzy Waśniewski, editors, Parallel Processing and Applied Mathematics, LNCS, pp. 613–622, Springer, 2014.
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In this work we present a new simple but efficient scheme -- Subsquares approach -- for development of algorithms for enclosing the solution set of overdetermined interval linear systems. We are going to show two algorithms based on this scheme and discuss their features. We start with a simple algorithm as a motivation, then we continue with an improved algorithm. Both algorithms can be easily parallelized. The features of both algorithms will be discussed and numerically tested.
@inCollection{HorHla2014a,
author = "Jaroslav Hor\'{a}{\v{c}}ek and Milan Hlad\'{\i}k",
title = "Subsquares approach -- A simple scheme for solving overdetermined interval linear systems",
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 = "613-622",
year = "2014",
doi = "10.1007/978-3-642-55195-6_58",
issn = "0302-9743",
isbn = "978-3-642-55194-9",
url = "http://dx.doi.org/10.1007/978-3-642-55195-6_58",
bib2html_dl_html = "http://dx.doi.org/10.1007/978-3-642-55195-6_58",
abstract = "In this work we present a new simple but efficient scheme -- Subsquares approach -- for development of algorithms for enclosing the solution set of overdetermined interval linear systems. We are going to show two algorithms based on this scheme and discuss their features. We start with a simple algorithm as a motivation, then we continue with an improved algorithm. Both algorithms can be easily parallelized. The features of both algorithms will be discussed and numerically tested.",
keywords = "Interval linear systems, interval enclosure, overdetermined systems, parallel computing",
}
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