Remarks on Computation and Error Analysis of Filon Quadrature
Summary :
A method of applying the fast Fourier transform (FFT) algorithm to Filon quadrature is presented. The quadrature formula can be reduced to a linear combination of two vectors to each of which the ordinary FFT algorithm is ready to be applied. An expression for the truncation error of Filon quadrature is then derived to examine the numerical errors of the formula. The experimental results showed that error terms of up to O(h7), where h is the length of subintervals for Filon numerical integration, are required to explain the numerical errors observed in the spectral analysis of the response of a single-pole system to a periodic rectangular wave.
- Publication
- IEICE TRANSACTIONS on transactions Vol.E72-E No.7 pp.813-818
- Publication Date
- 1989/07/25
- Publicized
- Online ISSN
- DOI
- Type of Manuscript
- PAPER
- Category
- Numerical Calculation and Mathematical Programming
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Kôki ABE, "Remarks on Computation and Error Analysis of Filon Quadrature" in IEICE TRANSACTIONS on transactions,
vol. E72-E, no. 7, pp. 813-818, July 1989, doi: .
Abstract: A method of applying the fast Fourier transform (FFT) algorithm to Filon quadrature is presented. The quadrature formula can be reduced to a linear combination of two vectors to each of which the ordinary FFT algorithm is ready to be applied. An expression for the truncation error of Filon quadrature is then derived to examine the numerical errors of the formula. The experimental results showed that error terms of up to O(h7), where h is the length of subintervals for Filon numerical integration, are required to explain the numerical errors observed in the spectral analysis of the response of a single-pole system to a periodic rectangular wave.
URL: https://global.ieice.org/en_transactions/transactions/10.1587/e72-e_7_813/_p
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@ARTICLE{e72-e_7_813,
author={Kôki ABE, },
journal={IEICE TRANSACTIONS on transactions},
title={Remarks on Computation and Error Analysis of Filon Quadrature},
year={1989},
volume={E72-E},
number={7},
pages={813-818},
abstract={A method of applying the fast Fourier transform (FFT) algorithm to Filon quadrature is presented. The quadrature formula can be reduced to a linear combination of two vectors to each of which the ordinary FFT algorithm is ready to be applied. An expression for the truncation error of Filon quadrature is then derived to examine the numerical errors of the formula. The experimental results showed that error terms of up to O(h7), where h is the length of subintervals for Filon numerical integration, are required to explain the numerical errors observed in the spectral analysis of the response of a single-pole system to a periodic rectangular wave.},
keywords={},
doi={},
ISSN={},
month={July},}
Copy
TY - JOUR
TI - Remarks on Computation and Error Analysis of Filon Quadrature
T2 - IEICE TRANSACTIONS on transactions
SP - 813
EP - 818
AU - Kôki ABE
PY - 1989
DO -
JO - IEICE TRANSACTIONS on transactions
SN -
VL - E72-E
IS - 7
JA - IEICE TRANSACTIONS on transactions
Y1 - July 1989
AB - A method of applying the fast Fourier transform (FFT) algorithm to Filon quadrature is presented. The quadrature formula can be reduced to a linear combination of two vectors to each of which the ordinary FFT algorithm is ready to be applied. An expression for the truncation error of Filon quadrature is then derived to examine the numerical errors of the formula. The experimental results showed that error terms of up to O(h7), where h is the length of subintervals for Filon numerical integration, are required to explain the numerical errors observed in the spectral analysis of the response of a single-pole system to a periodic rectangular wave.
ER -
English
