Milan Hladík. New operator and method for solving real preconditioned interval linear equations. SIAM J. Numer. Anal., 52(1):194–206, 2014.
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We deal with real preconditioned interval linear systems of equations. We present a new operator, which generalizes the interval Gauss--Seidel operator. Also, based on the new operator and properties of well-known methods, we propose a new algorithm, called the magnitude method. We illustrate by numerical examples that our approach outperforms some classical methods with respect to both time and sharpness of enclosures.
@article{Hla2014b,
author = "Milan Hlad\'{\i}k",
title = "New operator and method for solving real preconditioned interval linear equations",
journal = "SIAM J. Numer. Anal.",
fjournal = "SIAM Journal on Numerical Analysis",
volume = "52",
number = "1",
pages = "194-206",
year = "2014",
doi = "10.1137/130914358",
issn = "0036-1429",
bib2html_dl_html = "http://dx.doi.org/10.1137/130914358",
abstract = "We deal with real preconditioned interval linear systems of equations. We present a new operator, which generalizes the interval Gauss--Seidel operator. Also, based on the new operator and properties of well-known methods, we propose a new algorithm, called the magnitude method. We illustrate by numerical examples that our approach outperforms some classical methods with respect to both time and sharpness of enclosures.",
keywords = "Linear interval systems, Solution set, Interval matrix",
}
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