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2012 | 22 | 3 | 561-574
Tytuł artykułu

Enclosures for the solution set of parametric interval linear systems

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We investigate parametric interval linear systems of equations. The main result is a generalization of the Bauer-Skeel and the Hansen-Bliek-Rohn bounds for this case, comparing and refinement of both. We show that the latter bounds are not provable better, and that they are also sometimes too pessimistic. The presented form of both methods is suitable for combining them into one to get a more efficient algorithm. Some numerical experiments are carried out to illustrate performances of the methods.
Rocznik
Tom
22
Numer
3
Strony
561-574
Opis fizyczny
Daty
wydano
2012
otrzymano
2011-07-11
poprawiono
2011-11-24
Twórcy
  • Department of Applied Mathematics, Faculty of Mathematics and Physics, Charles University, Malostranské nám. 25, 118 00, Prague, Czech Republic
  • Faculty of Informatics and Statistics, University of Economics, nám. W. Churchilla 4, 13067, Prague, Czech Republic
Bibliografia
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  • Alefeld, G., Kreinovich, V. and Mayer, G. (2003). On the solution sets of particular classes of linear interval systems, Journal of Computational and Applied Mathematics 152(1-2): 1-15.
  • Alefeld, G. and Mayer, G. (1993). The Cholesky method for interval data, Linear Algebra and Its Applications 194: 161-182.
  • Alefeld, G. and Mayer, G. (2008). New criteria for the feasibility of the Cholesky method with interval data, SIAM Journal on Matrix Analysis and Applications 30(4): 1392-1405.
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  • Fiedler, M., Nedoma, J., Ramík, J., Rohn, J. and Zimmermann, K. (2006). Linear Optimization Problems with Inexact Data, Springer, New York, NY.
  • Garloff, J. (2010). Pivot tightening for the interval Cholesky method, Proceedings in Applied Mathematics and Mechanics 10(1): 549-550.
  • Hladík, M. (2008). Description of symmetric and skewsymmetric solution set, SIAM Journal on Matrix Analysis and Applications 30(2): 509-521.
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  • Meyer, C.D. (2000). Matrix Analysis and Applied Linear Algebra, SIAM, Philadelphia, PA.
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  • Popova, E. (2002). Quality of the solution sets of parameterdependent interval linear systems, Zeitschrift für Angewandte Mathematik und Mechanik 82(10): 723-727.
  • Popova, E.D. (2001). On the solution of parametrised linear systems, in W. Krämer and J.W. von Gudenberg (Eds.), Scientific Computing, Validated Numerics, Interval Methods, Kluwer, London, pp. 127-138.
  • Popova, E.D. (2004a). Parametric interval linear solver, Numerical Algorithms 37(1-4): 345-356.
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  • Rohn, J. (1989). Systems of linear interval equations, Linear Algebra and Its Applications 126(C): 39-78.
  • Rohn, J. (1993). Cheap and tight bounds: The recent result by E. Hansen can be made more efficient, Interval Computations (4): 13-21.
  • Rohn, J. (2004). A method for handling dependent data in interval linear systems, Technical Report 911, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague, http://uivtx.cs.cas.cz/˜rohn/publist/rp911.ps.
  • Rohn, J. (2010). An improvement of the Bauer-Skeel bounds, Technical Report V-1065, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague, http://uivtx.cs.cas.cz/˜rohn/publist/bauerskeel.pdf.
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  • Rump, S.M. (1994). Verification methods for dense and sparse systems of equations, in J. Herzberger (Ed.), Topics in Validated Computations, Studies in Computational Mathematics, Elsevier, Amsterdam, pp. 63-136.
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Typ dokumentu
Bibliografia
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Identyfikator YADDA
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