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. Parallel Computing, 34(6-8):392-410, 2008. - 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. - 4-04.221V
S.M. Rump, P. Zimmermann, S. Boldo, and G. Melquiond. Computing predecessor and successor in rounding to nearest. BIT Numerical Mathematics, 49(2):419-431, 2009.
- 4-04.222V
S.M. Rump. Inversion of extremely ill-conditioned matrices in floating-point. Japan J. Indust. Appl. Math. (JJIAM), 26:1-29, 2009.
- 4-04.223V
S.M. Rump, T. Ogita, and S. Oishi. Fast high precision summation. Appears in Nonlinear Theory and Its Applications (NOLTA), IEICE, 2010. - 4-04.224V
S.M. Rump. Ultimately Fast Accurate Summation. accepted for publication, 2009. - 4-04.225V
T. Nishi, T. Ogita, S. Oishi, and S. M. Rump. A Method for the Generation of a Class of Ill-conditioned Matrices. In 2008 International Symposium on Nonlinear Theory and its Applications, NOLTA'08, Budapest, Hungary, September 7-10, pages 53-56, 2008. - 4-04.226V
K. Ozaki, T. Ogita, S. M. Rump, and S. Oishi. Accurate matrix multiplication by using level 3 BLAS operation. In Proceedings of the 2008 International Symposium on Nonlinear Theory and its Applications, NOLTA'08, Budapest, Hungary, pages 508-511. IEICE, 2008. - 4-04.227V
S. Oishi, T. Ogita, and S. M. Rump. Iterative Refinement for Ill-conditioned Linear Equations. In 2008 International Symposium on Nonlinear Theory and its Applications, NOLTA'08, Budapest, Hungary, September 7-10, pages 516-519, 2008. - 4-04.231V
S.M. Rump, P. Zimmermann, S. Boldo, and G. Melquiond. Computing predecessor and successor in rounding to nearest. BIT Numerical Mathematics, 49(2):419-431, 2009. - 4-04.235V
S.M. Rump. Ultimately Fast Accurate Summation. SIAM Journal on Scientific Computing (SISC), 31(5):3466-3502, 2009. - 4-04.236V
S.M. Rump. Inversion of extremely ill-conditioned matrices in floating-point. Japan J. Indust. Appl. Math. (JJIAM), 26:249-277, 2009. - 4-04.237V
S.M. Rump. Error-Free Transformations and ill-conditioned problems. In Proceedings of the "International workshop on verified computations and related topics", University of Karlsruhe, March 7-10, 2009. - 4-04.238V
K. Ozaki, T. Ogita, S.M. Rump, and S. Oishi. Adaptive and Efficient Algorithm for 2D Orientation Problem. Japan J. Indust. Apl. Math., 26:215-231, 2009. - 4-04.239V
S. Oishi, T. Ogita, and S. M. Rump. Iterative Refinement for Ill-conditioned Linear Equations. Japan J. Indust. Appl. Math., 26(2):465-476, 2009. - 4-04.251V
S.M. Rump. Verification methods: Rigorous results using floating-point arithmetic. Acta Numerica, 19:287-449, 2010. - 4-04.253V
S.M. Rump, T. Ogita, and S. Oishi. Fast high precision summation. Appears in Nonlinear Theory and Its Applications (NOLTA), IEICE, 2010.
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