Milan Hladík. A contractor for the symmetric solution set. WASET, 71:94–99, 2010. Proceedings of the International Conference on Applied Mathematics and Engineering Mathematics, November 24-26, Venice, Italy
The symmetric solution set S is the set of all solutions to the linear systems Ax = b, where A is symmetric and lies between some given bounds A1 and A2, and b lies between b1 and b2. We present a contractor for S, which is an iterative method that starts with some initial enclosure of S (by means of a cartesian product of intervals) and sequentially makes the enclosure tighter. Our contractor is based on polyhedral approximation and solving a series of linear programs. Even though it does not converge to the optimal bounds in general, it may significantly reduce the overestimation. The efficiency is discussed by a number of numerical experiments.
@article{Hla2010l,
author = "Milan Hlad\'{\i}k",
title = "A contractor for the symmetric solution set",
journal = "WASET",
fjournal = "World Academy of Science, Engineering and Technology",
year = "2010",
volume = "71",
pages = "94-99",
note = "Proceedings of the International Conference on Applied Mathematics and Engineering Mathematics, November 24-26, Venice, Italy",
bib2html_dl_html = "http://www.waset.org/journals/waset/v71.php",
abstract = "The symmetric solution set S is the set of all solutions to the linear systems Ax = b, where A is symmetric and lies between some given bounds A1 and A2, and b lies between b1 and b2. We present a contractor for S, which is an iterative method that starts with some initial enclosure of S (by means of a cartesian product of intervals) and sequentially makes the enclosure tighter. Our contractor is based on polyhedral approximation and solving a series of linear programs. Even though it does not converge to the optimal bounds in general, it may significantly reduce the overestimation. The efficiency is discussed by a number of numerical experiments.
",
keywords = "linear interval systems, solution set, interval matrix,
symmetric matrix",
}
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