Fast Summation and Dot Product.
Mitarbeiter der Waseda University, Tokyo: Prof. Dr. Shin`Ichi Oishi (stellv. Leiter), Dr. T. Ogita, Dr. K. Ozaki. Auf der Basis von sogenannten fehlerfreien Transformationen werden schnelle Algorithmen entwickelt zur Summation von Gleitpunktzahlen und zur Berechnung von Skalarprodukten. Diese Grundroutinen des numerischen Rechnens wurden vielfach untersucht und zuletzt in XBLAS von renommierten Wissenschaftlern implementiert. Bereits jetzt wurden Algorithmen entwickelt, die unter allen Umständen bis auf den letzen Bit genaue Ergebnisse liefern und damit wesentlich genauer sind als XBLAS, die aber trotzdem etwa 40% schneller sind als XBLAS. Publikationen - 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. - 4-04.184V
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. - 4-04.187V
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. - 4-04.191V
T. Ogita, S.M. Rump, and S. Oishi. Accurate Sum and Dot Product. SIAM Journal on Scientific Computing (SISC), 26(6):1955-1988, 2005. - 4-04.206V
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. - 4-04.211V
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].
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