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Error bounds on complex floating-point multiplication

Brent, Richard; Percival, Colin; Zimmermann, Paul

Description

Given floating-point arithmetic with t-digit base-β significands in which all arithmetic operations are performed as if calculated to infinite precision and rounded to a nearest representable value, we prove that the product of complex values z0 and z1 can be computed with maximum absolute error |z0||z1|1/2β 1-t√5. In particular, this provides relative error bounds of 2-24√5 and 2-53√5. for IEEE 754 single and double precision arithmetic respectively, provided that overflow, underflow, and...[Show more]

CollectionsANU Research Publications
Date published: 2007-01-24
Type: Journal article
URI: http://hdl.handle.net/1885/100591
Source: Mathematics of Computation
DOI: 10.1090/S0025-5718-07-01931-X

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