A STOCHASTIC ROUNDOFF ERROR ANALYSIS FOR THE FAST FOURIER-TRANSFORM
A STOCHASTIC ROUNDOFF ERROR ANALYSIS FOR THE FAST FOURIER-TRANSFORM
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DOI：
10.1090/s0025-5718-1991-1068824-0
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发表时间：
1991-04-01
影响因子：
2
通讯作者：
CALVETTI, D
中科院分区：
文献类型：
--
作者：
CALVETTI, D
我们通过根据加法和乘法的基本运算的相对舍入误差的期望值和方差来估计伴随线性形式的期望值和方差来研究快速傅里叶变换的输出的准确性。 我们将结果与离散傅里叶变换直接算法的相应结果进行比较，并给出使用不同舍入方案时的相对性能的指示。 我们还介绍了为测试理论界限而进行的数值实验的结果，并讨论了它们的意义。
We study the accuracy of the output of the Fast Fourier Transform by estimating the expected value and the variance of the accompanying linear forms in terms of the expected value and variance of the relative roundoff errors for the elementary operations of addition and multiplication. We compare the results with the corresponding ones for the direct algorithm for the Discrete Fourier Transform, and we give indications of the relative performances when different rounding schemes are used. We also present the results of numerical experiments run to test the theoretical bounds and discuss their significance.