Tight interval inclusions with compensated algorithms

Abstract : Compensated algorithms consist in computing the rounding errors of individual operations and then adding them later to the computed result. This makes it possible to increase the accuracy of the computed result efficiently. Computing the rounding error of an individual operation is possible through the use of a so-called error-free transformation. In this talk, we show that it is possible to use compensated algorithms for having tight interval inclusions. We study compensated algorithms for summation, dot product and polynomial evaluation. We prove that the use of directed rounding makes it possible to get narrow inclusions with compensated algorithms. This is due to the fact that error-free transformations are no more exact but still sufficiently accurate to improve the numerical quality of results.
Document type :
Conference papers
Complete list of metadatas

Cited literature [5 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01963589
Contributor : Fabienne Jezequel <>
Submitted on : Monday, January 14, 2019 - 2:40:53 PM
Last modification on : Friday, July 5, 2019 - 3:26:03 PM

Identifiers

  • HAL Id : hal-01963589, version 1

Citation

Stef Graillat, Fabienne Jézéquel. Tight interval inclusions with compensated algorithms. 18th international symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2018), Sep 2018, Tokyo, Japan. pp.86-87. ⟨hal-01963589⟩

Share

Metrics

Record views

29

Files downloads

7