A note on regularity and positive definiteness of interval matrices

• Autorzy: Raena Farhadsefat , Taher Lotfi , Jiri Rohn
• 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.

Słowa kluczowe

EN

Interval matrix; Regularity condition; Positive definiteness

Kategorie tematyczne

• 65G40: General methods in interval analysis
• 15B48: Positive matrices and their generalizations; cones of matrices

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 1
• Strony: 322-328

Daty

wydano

2012-02-01

online

2011-12-09

Twórcy

autor

Raena Farhadsefat

• Islamic Azad University

autor

Taher Lotfi

• Islamic Azad University

autor

Jiri Rohn

• Czech Academy of Sciences

Bibliografia

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• [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

Identyfikatory

DOI

10.2478/s11533-011-0118-8