Article
Rundungsfehleranalyse einiger Verfahren zur Summation endlicher Summen
Abstract
deDer bei einer Summation auftretende Rundungsfehler kann als Maß für die Güte des verwendeten Verfahrens gelten. Im folgenden werden für mehrere Summierungsverfahren, unter anderem für das übliche und das Kahan‐Babuška‐Verfahren, a‐priori‐Schranken für diese Rundungsfehler angegeben und miteinander verglichen.
Abstract
enThe rounding‐error arising during summation can be interpreted as a measure for the quality of the procedure used. In the following, a‐priori‐bounds for this rounding‐error are used to compare several summation procedures, e.g. the common procedure and the method of Kahan‐Babuška.
Citing Literature
Number of times cited according to CrossRef: 24
- Antti Rantala, Pauli Pihajoki, Matias Mannerkoski, Peter H Johansson, Thorsten Naab, mstar – a fast parallelized algorithmically regularized integrator with minimum spanning tree coordinates, Monthly Notices of the Royal Astronomical Society, 10.1093/mnras/staa084, 492, 3, (4131-4148), (2020).
- Brett Neuman, Andy Dubois, Laura Monroe, Robert W Robey, Fast, good, and repeatable: Summations, vectorization, and reproducibility, The International Journal of High Performance Computing Applications, 10.1177/1094342020938425, (109434202093842), (2020).
- Marko Lange, Siegfried M. Rump, Verified inclusions for a nearest matrix of specified rank deficiency via a generalization of Wedin’s $$\sin (\theta )$$ theorem, BIT Numerical Mathematics, 10.1007/s10543-020-00827-y, (2020).
- Siegfried M. Rump, undefined, 2019 IEEE 26th Symposium on Computer Arithmetic (ARITH), 10.1109/ARITH.2019.00011, (1-14), (2019).
- Stef Graillat, Fabienne Jézéquel, Romain Picot, Numerical validation of compensated algorithms with stochastic arithmetic, Applied Mathematics and Computation, 10.1016/j.amc.2018.02.004, 329, (339-363), (2018).
- Giuseppe Bilotta, Vito Zago, Alexis Hérault, Design and Implementation of Particle Systems for Meshfree Methods with High Performance, High Performance Parallel Computing [Working Title], 10.5772/intechopen.73629, (2018).
- Jean-Michel Muller, Nicolas Brunie, Florent de Dinechin, Claude-Pierre Jeannerod, Mioara Joldes, Vincent Lefèvre, Guillaume Melquiond, Nathalie Revol, Serge Torres, Jean-Michel Muller, Nicolas Brunie, Florent de Dinechin, Claude-Pierre Jeannerod, Mioara Joldes, Vincent Lefèvre, Guillaume Melquiond, Nathalie Revol, Serge Torres, Enhanced Floating-Point Sums, Dot Products, and Polynomial Values, Handbook of Floating-Point Arithmetic, 10.1007/978-3-319-76526-6, (163-192), (2018).
- François Févotte, Bruno Lathuilière, Studying the Numerical Quality of an Industrial Computing Code: A Case Study on Code_aster, Numerical Software Verification, 10.1007/978-3-319-63501-9_5, (61-80), (2017).
- Sylvie Boldo, Stef Graillat, Jean-Michel Muller, On the Robustness of the 2Sum and Fast2Sum Algorithms, ACM Transactions on Mathematical Software, 10.1145/3054947, 44, 1, (1-14), (2017).
- Siegfried Michael Rump, Gleitkommaarithmetik auf dem Prüfstand, Jahresbericht der Deutschen Mathematiker-Vereinigung, 10.1365/s13291-016-0138-1, 118, 3, (179-226), (2016).
- Érik Martin-Dorel, Guillaume Melquiond, Jean-Michel Muller, Some issues related to double rounding, BIT Numerical Mathematics, 10.1007/s10543-013-0436-2, 53, 4, (897-924), (2013).
- Siegfried M. Rump, Accurate solution of dense linear systems, part I: Algorithms in rounding to nearest, Journal of Computational and Applied Mathematics, 10.1016/j.cam.2012.10.010, 242, (157-184), (2013).
- Florent de Dinechin, Christoph Lauter, Jean-Michel Muller, Serge Torres, On Ziv's rounding test, ACM Transactions on Mathematical Software, 10.1145/2491491.2491495, 39, 4, (1-19), (2013).
- Siegfried M. Rump, Verified Bounds for Least Squares Problems and Underdetermined Linear Systems, SIAM Journal on Matrix Analysis and Applications, 10.1137/110840248, 33, 1, (130-148), (2012).
- Nicolas Brunie, Florent de Dinechin, Benoit de Dinechin, undefined, 2011 Conference Record of the Forty Fifth Asilomar Conference on Signals, Systems and Computers (ASILOMAR), 10.1109/ACSSC.2011.6189977, (165-169), (2011).
- Siegfried M. Rump, Verification methods: Rigorous results using floating-point arithmetic, Acta Numerica, 10.1017/S096249291000005X, 19, (287-449), (2010).
- Siegfried M. Rump, Takeshi Ogita, Shin'ichi Oishi, Fast high precision summation, Nonlinear Theory and Its Applications, IEICE, 10.1587/nolta.1.2, 1, 1, (2-24), (2010).
- Siegfried M. Rump, Ultimately Fast Accurate Summation, SIAM Journal on Scientific Computing, 10.1137/080738490, 31, 5, (3466-3502), (2009).
- Siegfried M. Rump, Takeshi Ogita, Shin'ichi Oishi, Accurate Floating-Point Summation Part II: Sign, K -Fold Faithful and Rounding to Nearest , SIAM Journal on Scientific Computing, 10.1137/07068816X, 31, 2, (1269-1302), (2009).
- Siegfried M. Rump, Takeshi Ogita, Shin'ichi Oishi, Accurate Floating-Point Summation Part I: Faithful Rounding, SIAM Journal on Scientific Computing, 10.1137/050645671, 31, 1, (189-224), (2008).
- A. Klein, A Generalized Kahan-Babuška-Summation-Algorithm, Computing, 10.1007/s00607-005-0139-x, 76, 3-4, (279-293), (2005).
- Takeshi Ogita, Siegfried M. Rump, Shin'ichi Oishi, Accurate Sum and Dot Product, SIAM Journal on Scientific Computing, 10.1137/030601818, 26, 6, (1955-1988), (2005).
- Yong-Kang Zhu, Jun-Hai Yong, Guo-Qin Zheng, A New Distillation Algorithm for Floating-Point Summation, SIAM Journal on Scientific Computing, 10.1137/030602009, 26, 6, (2066-2078), (2005).
- Nicholas J. Higham, The Accuracy of Floating Point Summation, SIAM Journal on Scientific Computing, 10.1137/0914050, 14, 4, (783-799), (1993).
