This Article 
 Bibliographic References 
 Add to: 
On the Evaluation of Finite Hilbert Transforms
November/December 2007 (vol. 9 no. 6)
pp. 90-95
Mohankumar Nandagopal, Indira Gandhi Centre for Atomic Research
Natarajan Arunajadai, Indira Gandhi Centre for Atomic Research
The authors give a simple, efficient, and easy-to-implement prescription for numerically evaluating finite Hilbert transforms.

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.

Index Terms:
computing prescriptions, numerical recipes, transforms
Mohankumar Nandagopal, Natarajan Arunajadai, "On the Evaluation of Finite Hilbert Transforms," Computing in Science and Engineering, vol. 9, no. 6, pp. 90-95, Nov.-Dec. 2007, doi:10.1109/MCSE.2007.116
Usage of this product signifies your acceptance of the Terms of Use.