On the Cauchy transform and complex cubic splines

Authors

  • Crăciun Iancu “Babes-Bolyai” University, Cluj-Napoca, Romania
  • Tiberiu Oproiu “Babes-Bolyai” University, Cluj-Napoca, Romania
  • Alexandru Pop “Babes-Bolyai” University, Cluj-Napoca, Romania
  • Vasile Pop Cluj-Napoca, Romania

DOI:

https://doi.org/10.33993/jnaat321-734

Keywords:

Cauchy transform, Hölder condition, complex cubic spline
Abstract views: 260

Abstract

In this paper we approximate the Cauchy transform of a complex function on a simple closed curve, using an interpolation cubic spline function given by Iancu (1987).

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References

Ahlberg, J. H., Nilson, E. N. and Walsh, J. L., Complex cubic splines, Trans. Amer. Math. Soc., 129, pp. 391-413, 1967, https://doi.org/10.1090/S0002-9947-1967-0217484-X. DOI: https://doi.org/10.1090/S0002-9947-1967-0217484-X

Atkinson, K. E., The numerical solution of Fredholm integral equations of the second kind, SIAM J. Numer. Anal., 4, pp. 337-348, 1967, https://doi.org/10.1137/0704029. DOI: https://doi.org/10.1137/0704029

Atkinson, K. E., The numerical evaluation of the Cauchy transform on simple closed curves, SIAM J. Numer. Anal., 9, pp. 284-299, 1972, https://doi.org/10.1137/0709028. DOI: https://doi.org/10.1137/0709028

Atteia, M., Fage, C. and Gages, J., Etude et convergence des fonctions spline complexe, R.A.I.R.O. Analyse numerique, 18, no. 3, pp. 391-413, 1984. DOI: https://doi.org/10.1051/m2an/1984180302191

Chen Hanlin, Complex Spline Functions, Scientia Sinica, XXIV, no. 2, pp. 160-169, 1981.

Chien-Ke Lu, The Approximation of Cauhy-Type Integrals by some kinds of Interpolatory Splines, J. Approx. Theory, 36, pp. 197-212, 1982, https://doi.org/10.1016/0021-9045(82)90040-5. DOI: https://doi.org/10.1016/0021-9045(82)90040-5

Davis, P. J. and Rabinowitz, P., Numerical Integration Blaisdell, Waltham, Mass., 1967.

Gakhow, F. D., boundary Value Problem, Addison-Wesley, Reading, Mass., 1966. DOI: https://doi.org/10.1016/B978-0-08-010067-8.50007-4

Iancu, C., Sur une fonctions spline cubique complexe, "Babeş-Bolyai" Univ. Seminar on Numerical and Statistical Calculus, Preprint nr. 9, pp. 73-84, 1987.

Iancu, C., the error analysis in interpolation by complex spline fucntions, Studia Univ. "Babeş-Bolyai" Mathematica, XXXIV, no. 1, pp. 71-76, 1989.

Muskhelishvilli, N. I., Singular Integral Equations, Noordhoff, Groningen, Holand, 1953.

Stewart, C. E., On the Numerical Evaluation of Singular Integrals of Cauchy Type, J. Soc. Indust. Appl. Math., 8, no. 2, pp. 343-353, 1960, https://doi.org/10.1137/0108021. DOI: https://doi.org/10.1137/0108021

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Published

2003-02-01

How to Cite

Iancu, C., Oproiu, T., Pop, A., & Pop, V. (2003). On the Cauchy transform and complex cubic splines. Rev. Anal. Numér. Théor. Approx., 32(1), 63–68. https://doi.org/10.33993/jnaat321-734

Issue

Vol. 32 No. 1 (2003)

Section

Articles

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Copyright (c) 2015 Journal of Numerical Analysis and Approximation Theory

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