@inproceedings{d04f6fe999ad4442bfe938dc6dfe567c,
title = "Evaluating Straight-Line Programs over Balls",
abstract = "Interval arithmetic achieves numerical reliability for a wide range of applications, at the price of a performance penalty. For applications to homotopy continuation, one key ingredient is the efficient and reliable evaluation of complex polynomials represented by straight-line programs. This is best achieved using ball arithmetic, a variant of interval arithmetic. In this article, we describe strategies for reducing the performance penalty of basic operations on balls. We also show how to bound the effect of rounding errors at the global level of evaluating a straight-line program. This allows us to introduce a new and faster {"}transient{"} variant of ball arithmetic.",
keywords = "ball arithmetic, polynomial evaluation, software implementation",
author = "\{Van Der Hoeven\}, Joris and Gr{\'e}goire Lecerf",
note = "Publisher Copyright: {\textcopyright} 2016 IEEE.; 23rd IEEE Symposium on Computer Arithmetic, ARITH 2016 ; Conference date: 10-07-2016 Through 13-07-2016",
year = "2016",
month = sep,
day = "7",
doi = "10.1109/ARITH.2016.12",
language = "English",
series = "Proceedings - Symposium on Computer Arithmetic",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "142--149",
editor = "Javier Hormigo and Nathalie Revol and Paolo Montuschi and Stuart Oberman and Michael Schulte",
booktitle = "Proceedings - 2016 IEEE 23rd Symposium on Computer Arithmetic, ARITH 2016",
}