Recent results in fine-grained rounding error analysis

Dr. Claude-Pierre Jeannerod (Inria researcher in the AriC team at LIP - ENS de Lyon. )

Frank Adams Room 1,

Since the 1950s and Wilkinson's development of backward error analysis,
accuracy and stability results have been most often obtained using the
so-called standard model of floating-point arithmetic, and conveniently
expressed with bounds involving quantities of the form $\gamma_h :=
hu/(1-hu)$, where $u$ is the unit roundoff and $h$ typically depends on
the size of the problem. Recently, it was realized that for various core
algorithms these traditional worst-case bounds can be replaced by
simpler and sharper ones, sometimes without any size restriction like
$hu < 1$ or with $h$ provably minimal. This talk will survey these
results as well as some of the underlying techniques, and focus in
particular on the following aspects:

  1. The best-known error bounds and their conditions of applicability
          for various algorithms in linear algebra and complex arithmetic.
  2. The influence of some IEEE floating-point features (fused
          multiply-add, rounding modes) on fine-grained error analysis.
  3. The construction of certificates parametrized by the precision
          and aimed at showing that the bounds obtained are sharp or
          reasonably sharp.

 

Import this event to your Outlook calendar
▲ Up to the top