Roundoff errors in the fast computation of discrete convolutions

Karel Segeth

Aplikace matematiky (1981)

  • Volume: 26, Issue: 4, page 241-262
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Segeth, Karel. "Roundoff errors in the fast computation of discrete convolutions." Aplikace matematiky 26.4 (1981): 241-262. <http://eudml.org/doc/15199>.

@article{Segeth1981,
abstract = {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.},
author = {Segeth, Karel},
journal = {Aplikace matematiky},
keywords = {discrete convolution; fast Fourier transform; analysis of the roundoff errors; stochastic model; discrete convolution; fast Fourier transform; analysis of the roundoff errors; stochastic model},
language = {eng},
number = {4},
pages = {241-262},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Roundoff errors in the fast computation of discrete convolutions},
url = {http://eudml.org/doc/15199},
volume = {26},
year = {1981},
}

TY - JOUR
AU - Segeth, Karel
TI - Roundoff errors in the fast computation of discrete convolutions
JO - Aplikace matematiky
PY - 1981
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 26
IS - 4
SP - 241
EP - 262
AB - 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.
LA - eng
KW - discrete convolution; fast Fourier transform; analysis of the roundoff errors; stochastic model; discrete convolution; fast Fourier transform; analysis of the roundoff errors; stochastic model
UR - http://eudml.org/doc/15199
ER -

References

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