A STOCHASTIC ROUNDOFF ERROR ANALYSIS FOR THE CONVOLUTION
A STOCHASTIC ROUNDOFF ERROR ANALYSIS FOR THE CONVOLUTION
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DOI：
10.1090/s0025-5718-1992-1134719-8
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发表时间：
1992-10-01
影响因子：
2
通讯作者：
CALVETTI, D
中科院分区：
文献类型：
--
作者：
CALVETTI, D
我们研究了一种通过Radix-2快速傅里叶变换计算卷积的算法的精度。根据加法和乘法初等运算的相对舍入误差的期望值和方差，导出了相应线性形式的期望值和方差的上界。这些结果与直接计算卷积的两种算法的结果进行了比较，分别是通过荷马和和使用级联求和。
We study the accuracy of an algorithm which computes the convolution via Radix-2 fast Fourier transforms. Upper bounds are derived for 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. These results are compared with the corresponding ones for two algorithms computing the convolution directly, via Homer's sums and using cascade summation, respectively.