Exploiting structure in floating-point arithmetic

Claude-Pierre Jeannerod 1, 2
2 ARIC - Arithmetic and Computing
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : The analysis of algorithms in IEEE floating-point arithmetic is most often carried out via repeated applications of the so-called standard model, which bounds the relative error of each basic operation by a common epsilon depending only on the format. While this approach has been eminently useful for establishing many accuracy and stability results, it fails to capture most of the low-level features that make floating-point arithmetic so highly structured. In this paper, we survey some of those properties and how to exploit them in rounding error analysis. In particular, we review some recent improvements of several classical, Wilkinson-style error bounds from linear algebra and complex arithmetic that all rely on such structure properties.
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Mathematical Aspects of Computer and Information Sciences (MACIS), Nov 2015, Berlin, Germany. Springer, 9582, 2016, Lecture Notes in Computer Science. 〈10.1007/978-3-319-32859-1_2〉
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Claude-Pierre Jeannerod. Exploiting structure in floating-point arithmetic. Mathematical Aspects of Computer and Information Sciences (MACIS), Nov 2015, Berlin, Germany. Springer, 9582, 2016, Lecture Notes in Computer Science. 〈10.1007/978-3-319-32859-1_2〉. 〈hal-01247059〉

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