Tight interval inclusions with compensated algorithms

Abstract : Compensated algorithms consist in computing the rounding errors of individual operations and then adding them later on 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 article, we show that it is possible to use compensated algorithms for having tight interval inclusion. 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.
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Submitted on : Friday, December 21, 2018 - 2:26:23 PM
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Stef Graillat, Fabienne Jézéquel. Tight interval inclusions with compensated algorithms. IEEE Transactions on Computers, Institute of Electrical and Electronics Engineers, In press, ⟨10.1109/TC.2019.2924005⟩. ⟨hal-01963634v1⟩

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