메뉴 건너뛰기




Volumn 78, Issue 267, 2009, Pages 1629-1645

On the convergence rate of a modified fourier series

Author keywords

Function approximation; Orthogonal series; Oscillatory quadrature

Indexed keywords


EID: 67749097840     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-09-02204-2     Document Type: Article
Times cited : (24)

References (15)
  • 1
    • 0004245694 scopus 로고
    • Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables
    • #55, U.S. Govt. Printing Office, Washington, D.C. MR0167642 (29:4914)
    • Abramowitz, M., Stegun, I., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards Appl. Math. Series, #55, U.S. Govt. Printing Office, Washington, D.C., 1964. MR0167642 (29:4914)
    • (1964) National Bureau of Standards Appl. Math. Series
    • Abramowitz, M.1    Stegun, I.2
  • 2
    • 0037448182 scopus 로고    scopus 로고
    • Application of the combined nonlinear-condensation transformation to problems in statistical analysis and theoretical physics
    • Aksenov, S., Savageau, M.A., Jentschura, U.D., Becher, J., Soff, G., Mohr, P.J., Application of the combined nonlinear-condensation transformation to problems in statistical analysis and theoretical physics, Comp. Phys. Comm., 150 (2003) 1-20.
    • (2003) Comp. Phys. Comm. , vol.150 , pp. 1-20
    • Aksenov, S.1    Savageau, M.A.2    Jentschura, U.D.3    Becher, J.4    Soff, G.5    Mohr, P.J.6
  • 3
    • 14544287790 scopus 로고    scopus 로고
    • Trouble with Gegenbauer reconstruction for defeating Gibbs' phenomenon: Runge phenomenon in the diagonal limit of Gegenbauer polynomial approximations
    • MR2121910 (2005m:65005)
    • Boyd, J.P., Trouble with Gegenbauer reconstruction for defeating Gibbs' phenomenon: Runge phenomenon in the diagonal limit of Gegenbauer polynomial approximations, J. Comput. Physics, 204 (2005) 253-264. MR2121910 (2005m:65005)
    • (2005) J. Comput. Physics , vol.204 , pp. 253-264
    • Boyd, J.P.1
  • 4
    • 0005054331 scopus 로고
    • On a quadrature formula for trigonometric integrals
    • Filon, L.N.G., On a quadrature formula for trigonometric integrals, Proc. Roy. Soc. Edinburgh 49 (1928) 38-47.
    • (1928) Proc. Roy. Soc. Edinburgh , vol.49 , pp. 38-47
    • Filon, L.N.G.1
  • 5
    • 0031381548 scopus 로고    scopus 로고
    • On the Gibbs phenomenon and its resolution
    • MR1491051 (98m:42002)
    • Gottlieb, D., Shu, C.-W., On the Gibbs phenomenon and its resolution, SIAM Review 39 (1997) 644-668. MR1491051 (98m:42002)
    • (1997) SIAM Review , vol.39 , pp. 644-668
    • Gottlieb, D.1    Shu, C.-W.2
  • 6
    • 33749021121 scopus 로고    scopus 로고
    • On the evaluation of highly oscillatory integrals by analytic continuation
    • MR2231854 (2007d:41033)
    • Huybrechs, D., Vandewalle, S., On the evaluation of highly oscillatory integrals by analytic continuation, SIAM J. Numer. Anal. 44 (2006) 1026-1048. MR2231854 (2007d:41033)
    • (2006) SIAM J. Numer. Anal. , vol.44 , pp. 1026-1048
    • Huybrechs, D.1    Vandewalle, S.2
  • 8
    • 55849141690 scopus 로고    scopus 로고
    • From high oscillation to rapid approximation I: Modified Fourier expansions
    • MR2457350
    • Iserles, A., Nørsett, S.P., From high oscillation to rapid approximation I: Modified Fourier expansions, IMA J. Numer. Anal. 28 (2008), 862-887. MR2457350
    • (2008) IMA J. Numer. Anal. , vol.28 , pp. 862-887
    • Iserles, A.1    Nørsett, S.P.2
  • 9
    • 26944452051 scopus 로고    scopus 로고
    • Efficient quadrature of highly oscillatory integrals using derivatives
    • MR2147752 (2006b:65030)
    • Iserles, A., Nørsett, S.P., Efficient quadrature of highly oscillatory integrals using derivatives, Proceedings Royal Soc. A. 461 (2005) 1383-1399. MR2147752 (2006b:65030)
    • (2005) Proceedings Royal Soc. A , vol.461 , pp. 1383-1399
    • Iserles, A.1    Nørsett, S.P.2
  • 10
    • 55849105820 scopus 로고
    • On a special class of differential operators
    • Krein, M. G., On a special class of differential operators, Doklady AN USSR 2 (1935), 345-349.
    • (1935) Doklady AN USSR , vol.2 , pp. 345-349
    • Krein, M.G.1
  • 11
    • 84968468712 scopus 로고
    • Procedures for computing one and two-dimensional integrals of functions with rapid irregular oscillations
    • MR645668 (83a:65023)
    • Levin, D., Procedures for computing one and two-dimensional integrals of functions with rapid irregular oscillations, Math.Comp. 38 (1982), no. 158, 531-538. MR645668 (83a:65023)
    • (1982) Math. Comp. , vol.38 , Issue.158 , pp. 531-538
    • Levin, D.1
  • 13
    • 33645732701 scopus 로고    scopus 로고
    • Moment-free numerical integration of highly oscillatory functions
    • MR2218631 (2006k:65064)
    • Olver, S. Moment-free numerical integration of highly oscillatory functions, IMA J. Numer. Anal. 26 (2006) 213-227. MR2218631 (2006k:65064)
    • (2006) IMA J. Numer. Anal. , vol.26 , pp. 213-227
    • Olver, S.1
  • 14
    • 0004243541 scopus 로고
    • Cambridge University Press, Cambridge, MR604014 (82f:41001)
    • Powell, M.J.D. Approximation Theory and Methods, Cambridge University Press, Cambridge, 1981. MR604014 (82f:41001)
    • (1981) Approximation Theory and Methods
    • Powell, M.J.D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.