Iwona Skalna and Milan Hladík. A new method for computing a p-solution to parametric interval linear systems with affine-linear and nonlinear dependencies. BIT Numer. Math., 57(4):1109–1136, 2017.
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We propose a new approach to computing a parametric solution (the so-called p-solution) to parametric interval linear systems. Solving such system is an important part of many scientific and engineering problems involving uncertainties. The parametric solution has many useful properties. It permits to compute an outer solution, an inner estimate of the interval hull solution, and intervals containing the lower and upper bounds of the interval hull solution. It can also be employed for solving various constrained optimisation problems related to the parametric interval linear system. The proposed approach improves both outer and inner bounds for the parametric solution set. In this respect, the new approach is competitive to most of the existing methods for solving parametric interval linear systems. Improved bounds on the parametric solution set guarantees improved bounds for the solutions of related optimisation problems.
@article{SkaHla2017b,
author = "Iwona Skalna and Milan Hlad\'{\i}k",
title = "A new method for computing a p-solution to parametric interval linear systems with affine-linear and nonlinear dependencies",
journal = "BIT Numer. Math.",
fjournal = "BIT Numerical Mathematics",
volume = "57",
number = "4",
pages = "1109-1136",
year = "2017",
doi = "10.1007/s10543-017-0679-4",
issn = "1572-9125",
url = "https://link.springer.com/article/10.1007/s10543-017-0679-4",
bib2html_dl_html = "https://doi.org/10.1007/s10543-017-0679-4",
bib2html_dl_pdf = "http://rdcu.be/u7k1",
abstract = "We propose a new approach to computing a parametric solution (the so-called p-solution) to parametric interval linear systems. Solving such system is an important part of many scientific and engineering problems involving uncertainties. The parametric solution has many useful properties. It permits to compute an outer solution, an inner estimate of the interval hull solution, and intervals containing the lower and upper bounds of the interval hull solution. It can also be employed for solving various constrained optimisation problems related to the parametric interval linear system. The proposed approach improves both outer and inner bounds for the parametric solution set. In this respect, the new approach is competitive to most of the existing methods for solving parametric interval linear systems. Improved bounds on the parametric solution set guarantees improved bounds for the solutions of related optimisation problems.",
keywords = "Revised affine forms; Affine-interval iterative methods; Parametric interval linear systems; Parametric solution; Parametric linear programming",
}
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