Evaluating Straight-Line Programs over Balls

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 bes...

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Bibliographic Details
Main Authors: Van Der Hoeven, Joris, Lecerf, Gregoire
Format: Conference Proceeding
Language:English
Subjects:
ball arithmetic
C++ languages
Context
Hardware
Libraries
polynomial evaluation
Program processors
Reliability
software implementation
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Summary: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.
ISSN:1063-6889
DOI:10.1109/ARITH.2016.12