Self-validating methods.
Mitarbeiter der Waseda University, Tokyo: Prof. Dr. Shin`Ichi Oishi (stellv. Leiter), Prof. Dr. Tetsuo Nishi, Prof. Dr. Kunio Tanabe, Dr. S. Myajima, Dr. Nakaya, Dr. T. Ogita, Dr. T. Ohta, Dr. K. Ozaki, Dipl.-Ing. N. Yamanaka. 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. Publikationen - 4-04.171V
S.M. Rump and J. Zemke. On eigenvector bounds.BIT, 43:823-837, 2004. - 4-04.176V
T. Ogita, S.M. Rump, and S. Oishi. Accurate Sum and Dot Product with Applications. Proceedings of 2004 IEEE International Symposium on Computer Aided Control Systems Design, Taipei, pages 152-155, 2004. - 4-04.179V
S.M. Rump. Computer-Assisted Proofs I. Bulletin of the Japan Society for Industrial and Applied Mathematics (Bull. JSIAM), 14(3):214-223, 2004. - 4-04.180V
S.M. Rump. Computer-Assisted Proofs II. Bulletin of the Japan Society for Industrial and Applied Mathematics (Bull. JSIAM), 14(4):44-57, 2004. translated by T. Ogita. - 4-04.182V
S.M. Rump and T. Ogita. Super-Fast Validated Solution of Linear Systems. Journal of Computational and Applied Mathematics (JCAM), 199(2):199-206, 2006. Special issue on Scientific Computing, Computer Arithmetic, and Validated Numerics (SCAN 2004). - 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. - 4-04.191V
T. Ogita, S.M. Rump, and S. Oishi. Accurate Sum and Dot Product. SIAM Journal on Scientific Computing (SISC), 26(6):1955-1988, 2005. - 4-04.195V
C. Jansson, D. Chaykin, and C. Keil. Rigorous Error Bounds for the Optimal Value in Semidefinite Programming. SIAM Journal on Numerical Analysis (SINUM), 46(1) : 180-200, 2007. - 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. - 4-04.204V
S.M. Rump. Verification of Positive Definiteness. BIT Numerical Mathematics, 46:433-452, 2006. - 4-04.206V
S.M. Rump. Error bounds for extremely ill-conditioned problems. In Proceedings of 2006 International Symposium on Nonlinear Theory and its Applications, Bologna, Italy, September 11-14, 2006. - 4-04.209V
V. Kreinovich and S.M. Rump. Towards Optimal Use of Multi-Precision Arithmetic: A Remark. Reliable Computing, 12:365-369, 2006. - 4-04.210V
G. Alefeld, M.T. Nakao, and S.M. Rump. Preface. Journal of Computational and Applied Mathematics (JCAM), 199(2):197-198, 2006. Special issue on Scientific Computing, Computer Arithmetic, and Validated Numerics (SCAN 2004). - 4-04.211V
N. Yamanaka, T. Ogita, S.M. Rump, and S. Oishi. A Parallel Algorithm of Accurate Dot Product. accepted for publication, 2007. - 4-04.214V
K. Ozaki, T. Ogita, S. M. Rump, and S. Oishi. Accurate Matrix Multiplication with Multiple Floating-point Numbers. In Proceedings of 2007 International Symposium on Nonlinear Theory and its Applications, Vancouver, Canada, September 16-19, 2007. - 4-04.218V
S. Oishi, K. Tanabe, T. Ogita, and S.M. Rump. Convergence of Rump's method for inverting arbitrarily ill-conditioned matrices. J. Comput. Appl. Math., 205(1):533-544, 2007. - 4-04.219V
K. Ozaki, T. Ogita, S.M. Rump, and S. Oishi. Fast and robust algorithm for geometric predicates using floating-point arithmetic. Trans. JSIAM, 4(16):553-562, 2006. [in Japanese]. - 4-04.220V
T. Ogita, S.M. Rump, and S. Oishi. Verified solution of linear systems without directed rounding. Technical Report 2005-04, Advanced Research Institute for Science and Engineering, Waseda University, Tokyo, Japan, 2005.
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