From high oscillation to rapid approximation I: Modified Fourier expansions

IMA Journal of Numerical Analysis

Volumn 28, Issue 4, 2008, Pages 862-887

  Iserles, Arieh ^a   Nørsett, Syvert P ^b  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b NORWEGIAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Norway)

Author keywords

Convergence theorems; Filon type methods; Fourier expansion; Highly oscillatory quadrature

Indexed keywords

COMPUTATION THEORY;

ASYMPTOTIC SERIES; CONVERGENCE THEOREM; EXPANSION COEFFICIENTS; FILON-TYPE METHODS; FOURIER EXPANSION; OSCILLATORY QUADRATURE;

FOURIER SERIES;

EID: 55849141690     PISSN: 02724979     EISSN: 14643642     Source Type: Journal    
DOI: 10.1093/imanum/drn006     Document Type: Article

References (20)

1. ABRAMOWITZ, M. & STEGUN, I. A. (eds) (1964) Handbook of Mathematical Functions. Washington, DC: National Bureau of Standards.
2. DAVIES, E. B. (1995) Spectral Theory and Differential Operators. Cambridge Studies in Advanced Mathematics, vol. 42. Cambridge: Cambridge University Press.
3. HENRICI, P. (1986) Applied and Computational Complex Analysis, vol. 3. New York: John Wiley.
4. HUYBRECHS, D., ISERLES, A. & NØ RSETT, S. P. (2007) From high oscillation to rapid approximation IV: accelerating convergence. Technical Report NA2007/NA07. DAMTP, University of Cambridge.
5. HUYBRECHS, D., ISERLES, A. & NØ RSETT, S. P. (2008) From high oscillation to rapid approximation V: expansions in an equilateral triangle. Technical Report. DAMTP, University of Cambridge.
6. HUYBRECHS, D. & VANDEWALLE, S. (2008) On the evaluation of highly oscillatory integrals by analytic continuation. SIAM J. Numer. Anal. (to appear).
7. ISERLES, A. (2004) On the numerical quadrature of highly-oscillating integrals I: Fourier transforms. IMA J. Numer. Anal., 24, 365-391.
8. ISERLES, A. & NØRSETT, S. P. (2004) On quadrature methods for highly oscillatory integrals and their implementation. BIT, 44, 755-772.
9. ISERLES, A. & NØRSETT, S. P. (2005) Efficient quadrature of highly oscillatory integrals using derivatives. Proc. R. Soc. Lond. Ser A, 461, 1383-1399.
10. ISERLES, A. & NØRSETT, S. P. (2007a) From high oscillation to rapid approximation II: Birkhoff expansions. Technical Report. DAMTP, University of Cambridge.
11. ISERLES, A. & NØRSETT, S. P. (2007b) From high oscillation to rapid approximation III: multivariate expansions. Technical Report. DAMTP, University of Cambridge.
12. KANTOROVICH, L. V. & KRYLOV, V. I. (1958) Approximate Methods of Higher Analysis, 3rd edn. New York: Interscience.
13. KÖRNER, T. W. (1988) Fourier Analysis. Cambridge: Cambridge University Press.
14. KREIN, M. G. (1935) On a special class of differential operators. Dokl. Acad. Nauk. USSR, 2, 345-349.
15. LORENZ, G. G., JETTER, K. & RIEMENSCHNEIDER, S. D. (1983) Birkhoff Interpolation. London: Addison-Wesley.
16. OLVER, S. (2006) Moment-free numerical integration of highly oscillatory functions. IMA J. Numer, Anal., 26, 213-227.
17. RAINVILLE, E. D. (1960) Special Functions. New York: Macmillan.
18. RAO, K. R. & YIP, P. (1990) Discrete Cosine Transform: Algorithms, Advantages, Applications. Boston, MA: Academic Press.
19. ROACHE, P. B. (1978) A pseudo-spectral FFT technique for non-periodic problems. J. Comput. Phys., 27, 204-220.
20. YOUNG, R. M. (1980) An Introduction to Nonharmonic Fourier Series. New York: Academic Press.