Numerical Reproducibility and Parallel Computations: Issues for Interval Algorithms

What is called numerical reproducibility is the problem of getting the same result when the scientific computation is run several times, either on the same machine or on different machines, with different types and numbers of processing units, execution environments, computational loads, etc. This p...

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Bibliographic Details
Published in:IEEE transactions on computers Vol. 63; no. 8; pp. 1915 - 1924
Main Authors: Revol, Nathalie, Theveny, Philippe
Format: Journal Article
Language:English
Published: New York IEEE 01.08.2014
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Institute of Electrical and Electronics Engineers
Subjects:
Accuracy
Computation
Computer architecture
Computer Arithmetic
Computer Science
Computer simulation
Distributed, Parallel, and Cluster Computing
Floating point arithmetic
Inclusions
Instruction sets
Intervals
Mathematical models
Metals
Numerical models
Preserves
Registers
Reproducibility
Roundoff errors
floating-point arithmetic
numerical reproducibility
Interval arithmetic
rounding mode
parallel implementation
interval arithmetic
ISSN:0018-9340, 1557-9956
Online Access:Get full text
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Summary:What is called numerical reproducibility is the problem of getting the same result when the scientific computation is run several times, either on the same machine or on different machines, with different types and numbers of processing units, execution environments, computational loads, etc. This problem is especially stringent for HPC numerical simulations. In what follows, we identify the problems encountered when implementing interval routines in floating-point arithmetic. Some are well-known and common in numerical computations, some are specific to interval computations. We propose here a classification of floating-point issues by distinguishing their severity with respect to correctness and tightness of the computed interval result. In fact, interval computation can accommodate the lack of numerical reproducibility as long as it does not affect the inclusion property, which is the main property of interval arithmetic. Several ways to preserve the inclusion property are presented, on the example of the product of matrices with interval coefficients.
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ISSN:0018-9340
1557-9956
DOI:10.1109/TC.2014.2322593