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2012 | 10 | 1 | 322-328
Tytuł artykułu

A note on regularity and positive definiteness of interval matrices

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Języki publikacji
EN
Abstrakty
EN
We present a sufficient regularity condition for interval matrices which generalizes two previously known ones. It is formulated in terms of positive definiteness of a certain point matrix, and can also be used for checking positive definiteness of interval matrices. Comparing it with Beeck’s strong regularity condition, we show by counterexamples that none of the two conditions is more general than the other one.
Wydawca
Czasopismo
Rocznik
Tom
10
Numer
1
Strony
322-328
Opis fizyczny
Daty
wydano
2012-02-01
online
2011-12-09
Twórcy
autor
autor
Bibliografia
  • [1] Beeck H., Zur Problematik der Hüllenbestimmung von Intervallgleichungssystemen, In: Interval Mathematics, Karlsruhe, 1975, Lecture Notes in Comput. Sci., 29, Springer, Berlin, 1975, 150–159
  • [2] Fiedler M., Nedoma J., Ramík J., Rohn J., Zimmermann K., Linear Optimization Problems with Inexact Data, Springer, New York, 2006
  • [3] Garey M.R., Johnson D.S., Computers and Intractability, Ser. Books Math. Sci., W.H. Freeman and Company, San Francisco, 1979
  • [4] Horn R.A., Johnson C.R., Matrix Analysis, Cambridge University Press, Cambridge, 1985
  • [5] Oettli W., Prager W., Compatibility of approximate solution of linear equations with given error bounds for coefficients and right-hand sides, Numer. Math., 1964, 6, 405–409 http://dx.doi.org/10.1007/BF01386090
  • [6] Poljak S., Rohn J., Checking robust nonsingularity is NP-hard, Math. Control Signals Systems, 1993, 6(1), 1–9 http://dx.doi.org/10.1007/BF01213466
  • [7] Rex G., Rohn J., Sufficient conditions for regularity and singularity of interval matrices, SIAM J. Matrix Anal. Appl., 1999, 20(2), 437–445 http://dx.doi.org/10.1137/S0895479896310743
  • [8] Rohn J., Positive definiteness and stability of interval matrices, SIAM J. Matrix Anal. Appl., 1994, 15(1), 175–184 http://dx.doi.org/10.1137/S0895479891219216
  • [9] Rohn J., Forty necessary and sufficient conditions for regularity of interval matrices: a survey, Electron. J. Linear Algebra, 2009, 18, 500–512
  • [10] Rump S.M., Verification methods for dense and sparse systems of equations, In: Topics in Validated Computations, Oldenburg, 1993, Stud. Comput. Math., 5, North-Holland, Amsterdam, 1994, 63–135
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-011-0118-8
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