A Stochastic Roundoff Error Analysis for the Convolution
نویسنده
چکیده
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.
منابع مشابه
Continuous dependence on coefficients for stochastic evolution equations with multiplicative Levy Noise and monotone nonlinearity
Semilinear stochastic evolution equations with multiplicative L'evy noise are considered. The drift term is assumed to be monotone nonlinear and with linear growth. Unlike other similar works, we do not impose coercivity conditions on coefficients. We establish the continuous dependence of the mild solution with respect to initial conditions and also on coefficients. As corollaries of ...
متن کاملA Stochastic Roundoff Error Analysis for the Fast Fourier Transform
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...
متن کاملStochastic DEA with Using of Skew-Normal Distribution in Error Structure
The stochastic data envelopment analysis (SDEA) was developed considering the value ofinputs and outputs as random variables. Therefore, statistical distributions play an importantrole in this regard. The skew-normal (SN) distribution is a family of probability densityfunctions that is frequently used in practical situations. In this paper, we assume that the inputand output variables are skew-...
متن کاملA model for understanding numerical stability
We present a model of roundoff error analysis that combines simplicity with predictive power. Though not considering all sources of roundoff within an algorithm, the model is related to a recursive roundoff error analysis and therefore is capable of correctly predicting stability or instability of an algorithm. By means of nontrivial examples, such as the componentwise backward stability analys...
متن کاملLiu Estimates and Influence Analysis in Regression Models with Stochastic Linear Restrictions and AR (1) Errors
In the linear regression models with AR (1) error structure when collinearity exists, stochastic linear restrictions or modifications of biased estimators (including Liu estimators) can be used to reduce the estimated variance of the regression coefficients estimates. In this paper, the combination of the biased Liu estimator and stochastic linear restrictions estimator is considered to overcom...
متن کامل