Speaker: Nathalie Revol
Senior Scientist at INRIA and École Normale
Supérieure de Lyon, France
Title: Numerical Reproducibility and Parallel Computations: Issues for Interval Algorithms
Numerical reproducibility is the problem of obtaining the same result when a scientific computation is executed several times, either on the same machine or on different machines, with different types and numbers of processing units, execution environments, computational loads, etc. This problem is especially important for high-performance computing.
In this talk, the focus is on parallel implementations of interval arithmetic using floating-point arithmetic. The first part of this talk will be devoted to reproducibility issues in floating-point computations. These issues also impact interval computations, when interval arithmetic is implemented using floating-point arithmetic. For interval computations, numerical reproducibility is of course an issue for testing and debugging purposes. However, as long as the computed result encloses the exact (and unknown) result, the inclusion property, which is the main property of interval arithmetic, is satisfied and obtaining bitwise identical results may not be crucial. Still, implementation issues may invalidate the inclusion property. Several ways to preserve the inclusion property are presented and illustrated on an example involving a product of matrices with interval coefficients.
Joint work with Philippe Theveny.