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- W2762045278 abstract "Assuming floating-point arithmetic with a fused multiply-add operation and rounding nearest, the Cornea-Harrison-Tang method aims evaluate expressions of the form $ab+cd$ with high relative accuracy. In this paper we provide a rounding error analysis of this method that, unlike previous studies, is not restricted binary floating-point arithmetic but holds for any radix $beta$. We show first that an asymptotically optimal bound on the relative error of this method is $2u + 2u^2 + O(u^3)$, where $u= frac{1}{2}beta^{1-p}$ is the unit roundoff in radix $beta$ and precision $p$. Then we show that the possibility of removing the $O(u^2)$ term from this bound depends on the radix parity and the tie-breaking strategy used for rounding: if $beta$ is odd or rounding is to nearest even, then the simpler bound $2u$ is obtained, while if $beta$ is even and rounding is to nearest away, then there exist floating-point inputs $a,b,c,d$ that lead a relative error larger than $2u + frac{1}{beta}u^2$. All these results hold provided underflows and overflows do not occur and under some mild assumptions on $beta$ and $p$ satisfied by IEEE 754-2008 formats." @default.
- W2762045278 created "2017-10-20" @default.
- W2762045278 creator A5035039448 @default.
- W2762045278 date "2014-07-25" @default.
- W2762045278 modified "2023-09-27" @default.
- W2762045278 title "A rounding error analysis of the Cornea-Harrison-Tang method in radix $beta$" @default.
- W2762045278 hasPublicationYear "2014" @default.
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