The numerical stability of two-level and three-level iterative methods

1972 ◽  
Vol 12 (5) ◽  
pp. 140-154
Author(s):  
E.S. Nikolaev ◽  
A.A. Samarskii
2019 ◽  
Vol 214 ◽  
pp. 05025
Author(s):  
Hadrien Grasland ◽  
François Févotte ◽  
Bruno Lathuilière ◽  
David Chamont

Floating-point computations play a central role in scientific computing. Achieving high numerical stability in these computations affects not just correctness, but also computing efficiency, by accelerating the convergence of iterative methods and expanding the available choices of precision. The ACTS project aims at establishing an experiment-agnostic track reconstruction toolkit. It originates from the ATLAS Run2 tracking software and has already received strong adoption by FCC-hh. It is also being evaluated for possible use by the CLICdp and Belle 2 experiments. In this study, Verrou, a Valgrind-based tool for dynamic instrumentation of floating-point computations, was applied to the ACTS codebase for the dual purpose of evaluating its numerical stability and investigating possible avenues for use of reduced-precision arithmetic.


Author(s):  
Thamara Petroli ◽  
Marcos Arndt ◽  
Paulo de Oliveira Weinhardt ◽  
ROBERTO Dalledone Machado

2016 ◽  
Vol 106 (8) ◽  
pp. 538-545 ◽  
Author(s):  
Guanzhe Fa ◽  
Enrico Mazzarolo ◽  
Leqia He ◽  
Bruno Briseghella ◽  
Luigi Fenu ◽  
...  

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