Roundoff errors in the fast computation of discrete convolutions
Applications of Mathematics, Tome 26 (1981) no. 4, pp. 241-262.
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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.
DOI :
10.21136/AM.1981.103916
Classification :
42A15, 65F30, 65T05, 65T40
Mots-clés : discrete convolution; fast Fourier transform; analysis of the roundoff errors; stochastic model
Mots-clés : discrete convolution; fast Fourier transform; analysis of the roundoff errors; stochastic model
@article{10_21136_AM_1981_103916, author = {Segeth, Karel}, title = {Roundoff errors in the fast computation of discrete convolutions}, journal = {Applications of Mathematics}, pages = {241--262}, publisher = {mathdoc}, volume = {26}, number = {4}, year = {1981}, doi = {10.21136/AM.1981.103916}, mrnumber = {0623505}, zbl = {0474.65025}, language = {en}, url = {https://geodesic-test.mathdoc.fr/articles/10.21136/AM.1981.103916/} }
TY - JOUR AU - Segeth, Karel TI - Roundoff errors in the fast computation of discrete convolutions JO - Applications of Mathematics PY - 1981 SP - 241 EP - 262 VL - 26 IS - 4 PB - mathdoc UR - https://geodesic-test.mathdoc.fr/articles/10.21136/AM.1981.103916/ DO - 10.21136/AM.1981.103916 LA - en ID - 10_21136_AM_1981_103916 ER -
%0 Journal Article %A Segeth, Karel %T Roundoff errors in the fast computation of discrete convolutions %J Applications of Mathematics %D 1981 %P 241-262 %V 26 %N 4 %I mathdoc %U https://geodesic-test.mathdoc.fr/articles/10.21136/AM.1981.103916/ %R 10.21136/AM.1981.103916 %G en %F 10_21136_AM_1981_103916
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. https://geodesic-test.mathdoc.fr/articles/10.21136/AM.1981.103916/
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