Self-validating methods.

Mitarbeiter der Waseda University, Tokyo:

Prof. Dr. Shin`Ichi Oishi (stellv. Leiter), Dr. S. Migajima, Dr. T. Ogita, Dipl.-Ing. T. Ohta, Dipl.-Ing. K. Ozaki.

Es werden Methoden zur Verifikation von Fehlerschranken für Näherungslösungen numerischer Probleme entwickelt. Insbesondere werden große, spärlich besetzte lineare Gleichungssysteme, nichtlineare Gleichungssysteme, globale Optimierungsprobleme und schlecht konditionierte Probleme behandelt.

• 4-04.184V
  S.M. Rump. High Precision Evaluation of Nonlinear Functions. In Proceedings of 2005 International Symposium on Nonlinear Theory and its Applications, Bruge, Belgium, October 18-21, pages 733-736, 2005.
• 4-04.186V
  S.M. Rump. Computer-assisted proofs and Self-Validating Methods. In B. Einarsson, editor, Handbook on Acuracy and Reliability in Scientific Computation, pages 195-240. SIAM, 2005.
• 4-04.187V
  K. Ozaki, T. Ogita, S. Miyajima, S. Oishi, and S.M. Rump. Componentwise Verified Solutions of Linear System Suited for Java. In Proceedings of 2005 International Symposium on Nonlinear Theory and its Applications, Bruge, Belgium, October 18-21, pages 749-752, 2005.
• 4-04.188V
  K. Ozaki, T. Ogita, S. Miyajima, S. Oishi, and S.M. Rump. A Method of obtaining verified solutions for linear systems suited for Java. Journal of Computational and Applied Mathematics (JCAM), 199(2):337-344, 2006. Special issue on Scientific Computing, Computer Arithmetic, and Validated Numerics (SCAN 2004).
• 4-04.189V
  T. Ohta, T. Ogita, S.M. Rump, and S. Oishi. Numerical Verification Method for Arbitrarily Ill-conditioned Linear Systems. Trans. JSIAM, 15(3):269-287, 2005.
• 4-04.190V
  T. Ohta, T. Ogita, S.M. Rump, and S. Oishi. Numerical Method for Dense Linear Systems with Arbitrariliy Ill-conditioned Matrices. In Proceedings of 2005 International Symposium on Nonlinear Theory and its Applications, Bruge, Belgium, October 18-21, pages 745-748, 2005.
• 4-04.195V
  C. Jansson, D. Chaykin, and C. Keil. Rigorous Error Bounds for the Optimal Value in Semidefinite Programming. 2005. To appear in SIAM Journal on Numerical Analysis (SINUM), and electronically published http://www.optimization-online.org/DBHTML/2005/01/1047.html.
• 4-04.197V
  C. Jansson. Rigorous Results in Combinatorial Optimization. Algebraic and Numerical Algorithms and Computer-assisted Proofs, 2005. 8 pages.
• 4-04.198V
  C. Jansson. On Verifed Computation in Combinatorial Optimization. International Symposium on Nonlinear Theory and its Applications (NOLTA2005), Bruges, Belgium, pages 714-717, 2005.