Jaroslav Horáček and Milan Hladík. Computing enclosures of overdetermined interval linear systems. Reliab. Comput., 19(2):142–155, 2013.
This work considers special types of interval linear systems - overdetermined systems, systems consisting of more equations than variables. The solution set of an interval linear system is a collection of all solutions of all instances of an interval system. By the instance, we mean a point real system that emerges when we independently choose a real number from each interval coefficient of the interval system. Enclosing the solution set of these systems is in some ways more difficult than for square systems. This work presents various methods for computing enclosures of overdetermined interval linear systems. We would like to present them in an understandable way even for nonspecialists in the field of linear systems. The second goal is a numerical comparison of all mentioned methods on random interval linear systems regarding tightness of enclosures, computation times, and other special properties of methods.
@article{HorHla2013a,
author = "Jaroslav Hor\'{a}{\v{c}}ek and Milan Hlad\'{\i}k",
title = "Computing enclosures of overdetermined interval linear systems",
journal = "Reliab. Comput.",
fjournal = "Reliable Computing",
volume = "19",
number = "2",
pages = "142-155",
year = "2013",
issn = "1573-1340",
bib2html_dl_pdf = "http://interval.louisiana.edu/reliable-computing-journal/volume-19/reliable-computing-19-pp-142-155.pdf",
bib2html_dl_html = "http://interval.louisiana.edu/reliable-computing-journal/tables-of-contents.html#Volume_19",
abstract = "This work considers special types of interval linear systems - overdetermined systems, systems consisting of more equations than variables. The solution set of an interval linear system is a collection of all solutions of all instances of an interval system. By the instance, we mean a point real system that emerges when we independently choose a real number from each interval coefficient of the interval system. Enclosing the solution set of these systems is in some ways more difficult than for square systems. This work presents various methods for computing enclosures of overdetermined interval linear systems. We would like to present them in an understandable way even for nonspecialists in the field of linear systems. The second goal is a numerical comparison of all mentioned methods on random interval linear systems regarding tightness of enclosures, computation times, and other special properties of methods.",
keywords = "Interval linear systems, Enclosure methods, Overdetermined systems",
}
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