@misc{rev-the-14-aa-slides, author = {Nathalie Revol and Philippe Th{\'e}veny}, year = 2014, title = {Numerical Reproducibility of High-Performance Computations Using Floating-Point or Interval Arithmetic}, howpublished = {Slides of a presentation at the ICERM workshop \emph{Challenges in 21st Century Experimental Mathematical Computation}, 21-25 July 2014}, url = {https://icerm.brown.edu/materials/Slides/tw-14-5/Numerical_reproducibility_of_high-performance_computations_using_floating-point_or_interval_arithmetic_]_Nathalie_Revol,_INRIA.pdf}, comment = {Uses MFPI library for IA}, abstract = {My current effort: promote the use of interval arithmetic or some variants: Taylor models, affine arithmetic, through the development and implementation of methods that are not too slow compared to floating-point ones. Goal: slowdown factor less than 10. Interval matrix multiplication: slowdown factor less than 3. Interval linear system solving: slowdown factor around 15. Idea to gain performance (execution time): use optimized floating-point routines, such as BLAS. Disappointment due to the lack of numerical reproducibility.} }