The Use of Floating-Point and Interval Arithmetic in the Computation of Error Bounds

Three forms of interval floating-point arithmetic are defined in terms of absolute precision, relative precision, and combined absolute and relative precision. The absolute-precision form corresponds to the centered form of conventional rounded-interval arithmetic. The three forms are compared on th...

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Bibliographic Details
Published in:IEEE transactions on computers 1983-04, Vol.C-32 (4), p.411-417
Main Author: LOZIER, D. W
Format: Article
Language:English
Subjects:
Algorithmics. Computability. Computer arithmetics
Applied sciences
Arithmetic algorithms
Computer science
control theory
systems
error propagation
Exact sciences and technology
floating-point computation
inner-product accumulation
interval analysis
interval arithmetic
relative precision
rounding error analysis
Theoretical computing
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Description
Summary:Three forms of interval floating-point arithmetic are defined in terms of absolute precision, relative precision, and combined absolute and relative precision. The absolute-precision form corresponds to the centered form of conventional rounded-interval arithmetic. The three forms are compared on the basis of the number of floating-point operations needed to generate error bounds for inner-product accumulation.
ISSN:0018-9340
1557-9956
DOI:10.1109/TC.1983.1676245