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Roundoff errors in the fast computation of discrete convolutions
Applications of Mathematics, Tome 26 (1981) no. 4, pp. 241-262 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The efficient evaluation of a discrete convolution is usually carried out as a repated evaluation of a discrete convolution of a special type with the help of the fast Fourier transform. The paper is concerned with the analysis of the roundoff errors in the fast computation of this convolution. To obtain a comparison, the roundoff errors in the usual (direct) computation of this convolution are also considered. A stochastic model of the propagation of roundoff errors. is employed. The theoretical results are compared with the actual roundoff errors is employed. The theoretical results are compared with the actual roundoff errors occurring in the evaluation of a simple model discrete convolution.
The efficient evaluation of a discrete convolution is usually carried out as a repated evaluation of a discrete convolution of a special type with the help of the fast Fourier transform. The paper is concerned with the analysis of the roundoff errors in the fast computation of this convolution. To obtain a comparison, the roundoff errors in the usual (direct) computation of this convolution are also considered. A stochastic model of the propagation of roundoff errors. is employed. The theoretical results are compared with the actual roundoff errors is employed. The theoretical results are compared with the actual roundoff errors occurring in the evaluation of a simple model discrete convolution.
DOI : 10.21136/AM.1981.103916
Classification : 42A15, 65F30, 65T05, 65T40
Keywords: discrete convolution; fast Fourier transform; analysis of the roundoff errors; stochastic model 
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Segeth, Karel. Roundoff errors in the fast computation of discrete convolutions. Applications of Mathematics, Tome 26 (1981) no. 4, pp. 241-262. doi: 10.21136/AM.1981.103916

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