Skip to main content
Have a personal or library account? Click to login
Enclosures for the solution set of parametric interval linear systems Cover

Enclosures for the solution set of parametric interval linear systems

By:   
Open Access
|Sep 2012

References

  1. Alefeld, G., Kreinovich, V. and Mayer, G. (1997). On the shape of the symmetric, persymmetric, and skew-symmetric solution set,(3): 693-705.
  2. Alefeld, G., Kreinovich, V. and Mayer, G. (2003). On the solution sets of particular classes of linear interval systems,(1-2): 1-15.
  3. Alefeld, G. and Mayer, G. (1993). The Cholesky method for interval data,: 161-182.
  4. Alefeld, G. andMayer, G. (2008). New criteria for the feasibility of the Cholesky method with interval data,(4): 1392-1405.
  5. Beeck, H. (1975). Zur Problematik der H¨ullenbestimmung von Intervallgleichungssystem en,K. Nickel (Ed.),, Lecture Notes in Computer Science, Vol. 29, Springer, Berlin, pp. 150-159.
  6. Busłowicz, M. (2010). Robust stability of positive continuoustime linear systems with delays,(4): 665-670, DOI: 10.2478/v10006-010-0049-8.
  7. Fiedler, M., Nedoma, J., Ram´ık, J., Rohn, J. and Zimmermann, K. (2006)., Springer, New York, NY.
  8. Garloff, J. (2010). Pivot tightening for the interval Cholesky method,(1): 549-550.
  9. Hlad´ık, M. (2008). Description of symmetric and skewsymmetric solution set,(2): 509-521.
  10. Horn, R.A. and Johnson, C.R. (1985)., Cambridge University Press, Cambridge.
  11. Jansson, C. (1991). Interval linear systems with symmetric matrices, skew-symmetric matrices and dependencies in the right hand side,(3): 265-274.
  12. Kolev, L.V. (2004). A method for outer interval solution of linear parametric systems,(3): 227-239.
  13. Kolev, L.V. (2006). Improvement of a direct method for outer solution of linear parametric systems,(3): 193-202.
  14. Merlet, J.-P. (2009). Interval analysis for certified numerical solution of problems in robotics,(3): 399-412, DOI: 10.2478/v10006-009-0033-3.
  15. Meyer, C.D. (2000)., SIAM, Philadelphia, PA.
  16. Neumaier, A. (1990)., Cambridge University Press, Cambridge.
  17. Neumaier, A. (1999). A simple derivation of the Hansen-Bliek-Rohn-Ning-Kearfott enclosure for linear interval equations,(2): 131-136.
  18. Neumaier, A. and Pownuk, A. (2007). Linear systems with large uncertainties, with applications to truss structures,(2): 149-172.
  19. Ning, S. and Kearfott, R.B. (1997). A comparison of some methods for solving linear interval equations,(4): 1289-1305.
  20. Padberg, M. (1999).2nd Edn., Springer, Berlin.
  21. Popova, E. (2002). Quality of the solution sets of parameterdependent interval linear systems,(10): 723-727.
  22. Popova, E.D. (2001). On the solution of parametrised linear systems,W. Kr¨amer and J.W. von Gudenberg (Eds.),, Kluwer, London, pp. 127-138.
  23. Popova, E.D. (2004a). Parametric interval linear solver,(1-4): 345-356.
  24. Popova, E.D. (2004b). Strong regularity of parametric interval matrices,I. Dimovski (Ed.),, BAS, Sofia, pp. 446-451.
  25. Popova, E.D. (2006a). Computer-assisted proofs in solving linear parametric problems,, p. 35.
  26. Popova, E.D. (2006b). Webcomputing service framework,(3): 246-254.
  27. Popova, E.D. (2009). Explicit characterization of a class of parametric solution sets,(10): 1207-1216.
  28. Popova, E.D. and Kr¨amer, W. (2007). Inner and outer bounds for the solution set of parametric linear systems,(2): 310-316.
  29. Popova, E.D. and Kr¨amer, W. (2008). Visualizing parametric solution sets,(1): 95-115.
  30. Rex, G. and Rohn, J. (1998). Sufficient conditions for regularity and singularity of interval matrices,(2): 437-445.
  31. Rohn, J. (1989). Systems of linear interval equations,(C): 39-78.
  32. Rohn, J. (1993). Cheap and tight bounds: The recent result by E. Hansen can be made more efficient,(4): 13-21.
  33. Rohn, J. (2004). A method for handling dependent data in interval linear systems,, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague, http://uivtx.cs.cas.cz/˜rohn/publist/rp911.ps.
  34. Rohn, J. (2010). An improvement of the Bauer-Skeel bounds,, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague, http://uivtx.cs.cas.cz/˜rohn/publist/bauerskeel.pdf.
  35. Rump, S.M. (1983). Solving algebraic problems with high accuracy,U. Kulisch and W. Miranker (Eds.),, Academic Press, New York, NY, pp. 51-120.
  36. Rump, S.M. (1994). Verification methods for dense and sparse systems of equations,J. Herzberger (Ed.),, Studies in Computational Mathematics, Elsevier, Amsterdam, pp. 63-136.
  37. Rump, S.M. (2006). INTLAB-Interval Laboratory, the Matlab toolbox for verified computations, Version 5.3. http://www.ti3.tu-harburg.de/rump/intlab/.
  38. Rump, S.M. (2010). Verification methods: Rigorous results using floating-point arithmetic,: 287-449.
  39. Schrijver, A. (1998).Reprint Edn., Wiley, Chichester.
  40. Skalna, I. (2006). A method for outer interval solution of systems of linear equations depending linearly on interval parameters,(2): 107-120.
  41. Skalna, I. (2008). On checking the monotonicity of parametric interval solution of linear structural systems,R.
  42. Wyrzykowski, J. Dangarra, K. Karczewski and J. Wasniewski (Eds.),, Lecture Notes in Computer Science, Vol. 4967,
  43. Springer-Verlag, Berlin/Heidelberg, pp. 1400-1409.
  44. Stewart, G.W. (1998)., SIAM, Philadelphia, PA.
DOI: https://doi.org/10.2478/v10006-012-0043-4 | Journal eISSN: 2083-8492 | Journal ISSN: 1641-876X
Language: English
Page range: 561 - 574
Published on: Sep 28, 2012
Published by: University of Zielona Góra
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2012 Milan Hladík, published by University of Zielona Góra
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.