The Community for Technology Leaders
RSS Icon
Subscribe
Issue No.06 - November/December (2007 vol.9)
pp: 90-95
Mohankumar Nandagopal , Indira Gandhi Centre for Atomic Research
Natarajan Arunajadai , Indira Gandhi Centre for Atomic Research
ABSTRACT
The authors give a simple, efficient, and easy-to-implement prescription for numerically evaluating finite Hilbert transforms.
INDEX TERMS
computing prescriptions, numerical recipes, transforms
CITATION
Mohankumar Nandagopal, Natarajan Arunajadai, "On the Evaluation of Finite Hilbert Transforms", Computing in Science & Engineering, vol.9, no. 6, pp. 90-95, November/December 2007, doi:10.1109/MCSE.2007.116
REFERENCES
1. K.T.R. Davies et al., "The Mathematics of Principal Value Integrals and Applications to Nuclear Physics, Transport Theory, and Condensed Matter Physics," Mathematical Models and Methods in Applied Sciences, vol. 6, no. 6, 1996, pp. 833–885.
2. P. Rabinowitz,"The Numerical Evaluation of Cauchy Principal Value Integrals," Symp. Numerical Mathematics, Computer Science Dept., Univ. of Natal, Durban, 1978, pp. 53–82.
3. R. Piessens, "Numerical Evaluation of Cauchy Principal Values of Integrals," BIT, vol. 10, 1970, pp. 476–480.
4. D.B. Hunter, "Some Gauss-Type Formulae for the Evaluation of Cauchy Principal Value Integrals," Numerische Mathematik, vol. 19, 1972, pp. 419–424.
5. T. Hasegawa and T. Torii, "An Automatic Quadrature for Cauchy Principal Value Integrals," Mathematics of Computation, vol. 56, no. 194, 1991, pp. 741–754.
6. C. Schwartz, "Numerical Integration of Analytic Functions," J. Computational Physics, vol. 4, 1969, pp. 19–29.
7. M. Iri, S. Moriguti, and Y. Takasawa, "On a Certain Quadrature Formula," J. Computational and Applied Mathematics, vol. 17, 1987, pp. 3–20.
8. H. Takahasi and M. Mori, "Double Exponential Formulas for Numerical Integration," Publications of Research Inst. Mathematical Sciences, Kyoto Univ., vol. 9, 1974, pp. 721–741.
9. E. Venturino, "On Solving Singular Integral Equations via a Hyperbolic Tangent Quadrature Rule," Mathematics of Computation, vol. 47, no. 175, 1986, pp. 159–167.
10. N. Mohankumar and A. Natarajan, "An Error Analysis of the Cauchy Principal Value Integral Evaluation by the IMT Scheme," Proc. Royal Soc. London, series A, vol. 454, 1998, pp. 139–145.
11. P.J. Davis and P. Rabinowitz, Methods of Numerical Integration, 2nd ed., Academic Press, 1984.
12. B. Bialecki, "A modified Sinc-Quadrature Rule for Functions with Poles near the Arc of Integration," BIT, vol. 29, 1989, pp. 464–476.
13. R. Piessens et al., QUADPACK, A Subroutine Package for Automatic Integration, Springer-Verlag, 1983.
14. A. Natarajan and N. Mohankumar, "A Comparison of Some Quadrature Methods for Approximating Cauchy Principal Value Integrals," J. Computational Physics, vol. 116, 1995, pp. 365–368.
15. W.J. Thompson, "Principal-Value Integrals by a Simple and Accurate Finite-Interval Method," Computers in Physics, vol. 12, no. 1, 1998, pp. 94–96.
16. J.V. Noble, "Gauss-Legendre Principal Value Integration," Computing in Science &Eng., vol. 2, no. 1, 2000, pp. 92–95.
17 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool