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Preface
A Gaussian quadrature rule for oscillatory integrals on a bounded interval
1. | Dept. Computer Science, University of Leuven, Belgium, BE-3001 Heverlee, Belgium, Belgium, Belgium, Belgium |
References:
[1] |
A. Asheim and D. Huybrechs, Gaussian quadrature for oscillatory integral transforms, IMA J. Numer. Anal, (2013).
doi: 10.1093/imanum/drs060. |
[2] |
P. Bleher and A. Its, Asymptotics of the partition function of a random matrix model, in "Ann. Inst. Fourier," 55 (2005), 1943-2000.
doi: 10.5802/aif.2147. |
[3] |
L. Filon, On a quadrature formula for trigonometric integrals, Proc. Roy. Soc. Edinburgh, 49 (1928), 38-47. |
[4] |
W. Gautschi, "Orthogonal Polynomials: Computation and Approximation," Oxford University Press, 2004. |
[5] |
D. Huybrechs and S. Olver, Superinterpolation in highly oscillatory quadrature, Found. Comput. Math, 12 (2012), 203-228.
doi: 10.1007/s10208-011-9102-8. |
[6] |
D. Huybrechs and S. Vandewalle, On the evaluation of highly oscillatory integrals by analytic continuation, SIAM J. Numer. Anal., 44 (2006), 1026-1048.
doi: 10.1137/050636814. |
[7] |
A. Iserles, Think globally, act locally: Solving highly-oscillatory ordinary differential equations, Appl. Numer. Math., 43 (2002), 145-160.
doi: 10.1016/S0168-9274(02)00122-8. |
[8] |
A. Iserles, On the numerical quadrature of highly-oscillating integrals I: Fourier transforms, IMA J. Numer. Anal., 24 (2004), 365-391.
doi: 10.1093/imanum/24.3.365. |
[9] |
A. Iserles and S. Nørsett, Efficient quadrature of highly oscillatory integrals using derivatives, Proc. R. Soc. A, 461 (2005), 1383-1399.
doi: 10.1098/rspa.2004.1401. |
[10] |
A. Iserles and S. P. Nørsett, On quadrature methods for highly oscillatory integrals and their implementation, BIT, 44 (2004), 755-772.
doi: 10.1007/s10543-004-5243-3. |
[11] |
A. Iserles and S. P. Nørsett, On the computation of highly oscillatory multivariate integrals with stationary points, BIT, 46 (2006), 549-566.
doi: 10.1007/s10543-006-0071-2. |
[12] |
A. Iserles and S. P. Nørsett, Quadrature methods for multivariate highly oscillatory integrals using derivatives, Math. Comp., 75 (2006), 1233-1258.
doi: 10.1090/S0025-5718-06-01854-0. |
[13] |
L. G. Ixaru and B. Paternoster, A Gauss quadrature rule for oscillatory integrands, Comput. Phys. Commun., 133 (2001), 177-188.
doi: 10.1016/S0010-4655(00)00173-9. |
[14] |
V. Ledoux and M. Van Daele, Interpolatory quadrature rules for oscillatory integrals, J. Sci. Comput., 53 (2012), 586-607.
doi: 10.1007/s10915-012-9589-4. |
[15] |
D. Levin, Fast integration of rapidly oscillatory functions, J. Comput. Appl. Math., 67 (1996), 95-101.
doi: 10.1016/0377-0427(94)00118-9. |
[16] |
J. L. López and N. M. Temme, Two-point Taylor expansions of analytic functions, Stud. Appl. Math., 109 (2002), 297-311.
doi: 10.1111/1467-9590.00225. |
[17] |
F. Olver, D. Lozier, R. Boisvert and C. Clark, "NIST Handbook of Mathematical Functions," Cambridge University Press, 2010. |
[18] |
S. Olver, Moment-free numerical integration of highly oscillatory functions, IMA J. Numer. Anal., 26 (2006), 213-227.
doi: 10.1093/imanum/dri040. |
[19] |
S. Olver, Fast, numerically stable computation of oscillatory integrals with stationary points, BIT, 50 (2010), 149-171.
doi: 10.1007/s10543-010-0251-y. |
show all references
References:
[1] |
A. Asheim and D. Huybrechs, Gaussian quadrature for oscillatory integral transforms, IMA J. Numer. Anal, (2013).
doi: 10.1093/imanum/drs060. |
[2] |
P. Bleher and A. Its, Asymptotics of the partition function of a random matrix model, in "Ann. Inst. Fourier," 55 (2005), 1943-2000.
doi: 10.5802/aif.2147. |
[3] |
L. Filon, On a quadrature formula for trigonometric integrals, Proc. Roy. Soc. Edinburgh, 49 (1928), 38-47. |
[4] |
W. Gautschi, "Orthogonal Polynomials: Computation and Approximation," Oxford University Press, 2004. |
[5] |
D. Huybrechs and S. Olver, Superinterpolation in highly oscillatory quadrature, Found. Comput. Math, 12 (2012), 203-228.
doi: 10.1007/s10208-011-9102-8. |
[6] |
D. Huybrechs and S. Vandewalle, On the evaluation of highly oscillatory integrals by analytic continuation, SIAM J. Numer. Anal., 44 (2006), 1026-1048.
doi: 10.1137/050636814. |
[7] |
A. Iserles, Think globally, act locally: Solving highly-oscillatory ordinary differential equations, Appl. Numer. Math., 43 (2002), 145-160.
doi: 10.1016/S0168-9274(02)00122-8. |
[8] |
A. Iserles, On the numerical quadrature of highly-oscillating integrals I: Fourier transforms, IMA J. Numer. Anal., 24 (2004), 365-391.
doi: 10.1093/imanum/24.3.365. |
[9] |
A. Iserles and S. Nørsett, Efficient quadrature of highly oscillatory integrals using derivatives, Proc. R. Soc. A, 461 (2005), 1383-1399.
doi: 10.1098/rspa.2004.1401. |
[10] |
A. Iserles and S. P. Nørsett, On quadrature methods for highly oscillatory integrals and their implementation, BIT, 44 (2004), 755-772.
doi: 10.1007/s10543-004-5243-3. |
[11] |
A. Iserles and S. P. Nørsett, On the computation of highly oscillatory multivariate integrals with stationary points, BIT, 46 (2006), 549-566.
doi: 10.1007/s10543-006-0071-2. |
[12] |
A. Iserles and S. P. Nørsett, Quadrature methods for multivariate highly oscillatory integrals using derivatives, Math. Comp., 75 (2006), 1233-1258.
doi: 10.1090/S0025-5718-06-01854-0. |
[13] |
L. G. Ixaru and B. Paternoster, A Gauss quadrature rule for oscillatory integrands, Comput. Phys. Commun., 133 (2001), 177-188.
doi: 10.1016/S0010-4655(00)00173-9. |
[14] |
V. Ledoux and M. Van Daele, Interpolatory quadrature rules for oscillatory integrals, J. Sci. Comput., 53 (2012), 586-607.
doi: 10.1007/s10915-012-9589-4. |
[15] |
D. Levin, Fast integration of rapidly oscillatory functions, J. Comput. Appl. Math., 67 (1996), 95-101.
doi: 10.1016/0377-0427(94)00118-9. |
[16] |
J. L. López and N. M. Temme, Two-point Taylor expansions of analytic functions, Stud. Appl. Math., 109 (2002), 297-311.
doi: 10.1111/1467-9590.00225. |
[17] |
F. Olver, D. Lozier, R. Boisvert and C. Clark, "NIST Handbook of Mathematical Functions," Cambridge University Press, 2010. |
[18] |
S. Olver, Moment-free numerical integration of highly oscillatory functions, IMA J. Numer. Anal., 26 (2006), 213-227.
doi: 10.1093/imanum/dri040. |
[19] |
S. Olver, Fast, numerically stable computation of oscillatory integrals with stationary points, BIT, 50 (2010), 149-171.
doi: 10.1007/s10543-010-0251-y. |
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