Milan Hladík. On relation between P-matrices and regularity of interval matrices. In Natália Bebiano, editor, Applied and Computational Matrix Analysis, Springer Proceedings in Mathematics & Statistics, pp. 27–35, Springer, 2017.
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We explore new results between P-matrix property and regularity of interval matrices. In particular, we show that an interval matrix is regular in and only if some special matrices constructed from its center and radius matrices are P-matrices. We also investigate the converse direction. We reduce the problem of checking P-matrix property to regularity of a special interval matrix. Based on this reduction, novel sufficient condition for a P-matrix property is derived, and its strength is inspected. We also state a new observation to interval P-matrices.
In the formulation of Theorem 5, matrix A should be real, not interval.
@inCollection{Hla2017b,
author = "Milan Hlad\'{\i}k",
title = "On relation between {P}-matrices and regularity of interval matrices",
editor = "Bebiano, Nat{\'a}lia",
booktitle = "Applied and Computational Matrix Analysis",
fbooktitle = "Applied and Computational Matrix Analysis. MAT-TRIAD, Coimbra, Portugal, September 2015 Selected, Revised Contributions",
publisher = "Springer",
series = "Springer Proceedings in Mathematics \& Statistics",
volume = "192",
pages = "27-35",
year = "2017",
doi = "10.1007/978-3-319-49984-0_2",
isbn = "978-3-319-49984-0",
issn = "2194-1009",
url = "http://link.springer.com/chapter/10.1007/978-3-319-49984-0_2",
bib2html_dl_html = "http://dx.doi.org/10.1007/978-3-319-49984-0_2",
abstract = "We explore new results between P-matrix property and regularity of interval matrices. In particular, we show that an interval matrix is regular in and only if some special matrices constructed from its center and radius matrices are P-matrices. We also investigate the converse direction. We reduce the problem of checking P-matrix property to regularity of a special interval matrix. Based on this reduction, novel sufficient condition for a P-matrix property is derived, and its strength is inspected. We also state a new observation to interval P-matrices.",
bib2html_errata = "In the formulation of Theorem 5, matrix A should be real, not interval.",
keywords = "Interval matrix; P-matrix; Interval analysis; Linear complementarity",
}
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