Iwona Skalna and Milan Hladík. Enhancing monotonicity checking in parametric interval linear systems. In N. Damouche M. Martel and J. A. Dit Sandretto, editors, TNC'18. Trusted Numerical Computations, Kalpa Publications in Computing, pp. 70–83, EasyChair, 2018.
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Solving systems of parametric linear equations with parameters varying within closed intervals is a hard computational problem. However, we may reduce the problem dimension and thus make the problem more tractable by utilizing the monotonicity of the solution components with respect to the parameters. In this paper, we propose two improvements of the standard monotonicity checking techniques. The first improvement relies on creating a system with original variables and their derivatives as unknowns, and the second one employs the so-called p-solution. By a series of numerical experiments we show that the improved monotonicity approach outperforms the standard one.
@inCollection{SkaHla2018a,
author = "Iwona Skalna and Milan Hlad\'{\i}k",
title = "Enhancing monotonicity checking in parametric interval linear systems",
editor = "M. Martel, N. Damouche and J. A. Dit Sandretto",
feditor = "Matthieu Martel and Nasrine Damouche and Julien Alexandre Dit Sandretto",
booktitle = "TNC'18. Trusted Numerical Computations",
publisher = "EasyChair",
series = "Kalpa Publications in Computing",
volume = "8",
pages = "70-83",
year = "2018",
doi = "10.29007/1vkp",
issn = "2515-1762",
url = "https://easychair.org/publications/paper/B8Cn",
bib2html_dl_html = "https://doi.org/10.29007/1vkp",
abstract = "Solving systems of parametric linear equations with parameters varying within closed intervals is a hard computational problem. However, we may reduce the problem dimension and thus make the problem more tractable by utilizing the monotonicity of the solution components with respect to the parameters. In this paper, we propose two improvements of the standard monotonicity checking techniques. The first improvement relies on creating a system with original variables and their derivatives as unknowns, and the second one employs the so-called p-solution. By a series of numerical experiments we show that the improved monotonicity approach outperforms the standard one.",
keywords = "p-solution; Monotonicity approach; Parametric interval linear systems",
}
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