Snehashish Chakraverty, Milan Hladík, and Diptiranjan Behera. Formal solution of an interval system of linear equations with an application in static responses of structures with interval forces. Appl. Math. Model., 50:105–117, 2017.
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We are concerned with the so called formal solution of an interval system of linear equations. We focus on the case where the coefficient matrix is deterministic (real) and the right-hand side is an interval vector. We show that the set of formal solutions represents a convex polyhedral set. We propose new properties of the formal solution related to its existence, uniqueness and robustness. As particular classes of problems we investigate also the situation where the coefficient matrix is an M-matrix or H-matrix. Example problems related to the structures, such as 6-bar truss and a rectangular sheet, are solved to illustrate the computational aspects of the methods.
@article{ChakHla2017b,
author = "Snehashish Chakraverty and Milan Hlad\'{\i}k and Diptiranjan Behera",
title = "Formal solution of an interval system of linear equations with an application in static responses of structures with interval forces",
journal = "Appl. Math. Model.",
fjournal = "Applied Mathematical Modelling",
volume = "50",
pages = "105-117",
year = "2017",
doi = "10.1016/j.apm.2017.05.010",
issn = "0307-904X",
bib2html_dl_html = "https://doi.org/10.1016/j.apm.2017.05.010",
abstract = "We are concerned with the so called formal solution of an interval system of linear equations. We focus on the case where the coefficient matrix is deterministic (real) and the right-hand side is an interval vector. We show that the set of formal solutions represents a convex polyhedral set. We propose new properties of the formal solution related to its existence, uniqueness and robustness. As particular classes of problems we investigate also the situation where the coefficient matrix is an M-matrix or H-matrix. Example problems related to the structures, such as 6-bar truss and a rectangular sheet, are solved to illustrate the computational aspects of the methods.",
keywords = "Interval system of linear equations; Interval number; Truss; Rectangular sheet",
}
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