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by Unit Mixte, Recherche Cnrs-inria-ens Lyon, Cole Normale Suprieure De Lyon, Cole Normale Suprieure De Lyon, N. Revol, N. Revol, K. Makino, K. Makino, M. Berz, M. Berz
ftp://ftp.ens-lyon.fr/pub/LIP/Rapports/RR/RR2003/RR2003-11.ps.gz
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Abstract:

Taylor models and oating-point arithmetic: proof that arithmetic operations are validated in COSY

Citations

479 Accuracy and stability of numerical algorithms – Higham - 1996
199 What every computer scientist should know about floating-point arithmetic – Goldberg - 1991
64 A floating-point technique for extending the available precision – Dekker - 1971
29 Floating-Point Computation – Sterbenz - 1974
7 Forward algorithms for high orders and many variables with application to beam physics – Berz - 1991
7 Rigorous Analysis of Nonlinear Motion in Particle Accelerators – Makino - 1998
5 A proposed radix-and-word-length-independent standard for floating-point arithmetic – Cody, Coonen, et al. - 1984
4 Adaptive precision oating-point arithmetic and fast robust geometric predicates – Shewchuk - 1997
3 Veri high-order inversion of functional dependencies and interval Newton methods – Berz, Hoefkens
3 Verification of Invertibility of Complicated Functions over Large Domains – Hoefkens, Berz - 2002
2 Modern Map Methods in Particle Beam Physics – Berz - 1999
2 COSY INFINITY Version 8.1 - programming manual – Berz, Hoefkens - 2002
2 New methods for high-dimensional veried quadrature – Berz, Makino - 1999
2 Methods for range bounding by Taylor models: LDB, QDB and related algorithms. submitted. Proof that arithmetic operations are validated – Makino, Berz
1 Veried integration of ODEs and ows using dierential algebraic methods on high-order Taylor models – Berz, Makino - 1998
1 Higher order veried inclusions of multidimensional systems by Taylor models. Nonlinear Analysis – Makino, Berz - 2001
1 Algorithms for arbitrary precision oating-point arithmetic – Priest - 1991
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