Error bounds on complex floating-point multiplication
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]
|Collections||ANU Research Publications|
|Source:||Mathematics of Computation|
|01_Brent_Error_Bounds_2007.pdf||259.2 kB||Adobe PDF|
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