Interpolation on Arbitrary Regions in the Complex Plane

Applied and Computational Harmonic Analysis

Volumn 4, Issue 3, 1997, Pages 264-292

  Ma, J ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0346509527     PISSN: 10635203     EISSN: None     Source Type: Journal    
DOI: 10.1006/acha.1997.0215     Document Type: Article

References (26)

1. M. Abramowitz and I. A. Stegun (Ed.), "Handbook of Mathematical Functions," Applied Mathematics Series, Vol. 55, National Bureau of Standards, Washington, DC, 1964.
2. G. R. Baker and M. J. Shelley, On the connection between thin vortex layers and vortex sheets, J. Fluid Mech. 215 (1990), 261-294.
3. B. Bialecki and Y. Yan, A rectangular quadrature method for logarithmically singular integral equations of the first kind, J. Integral Equations Appl. 4 (1992), 377-369.
4. J. Carrier, L. Greengard, and V. Rokhlin, A fast adaptive multipole algorithm for particle simulations, SIAM J. Sci. Stat. Comput. 9, No. 4 (1988).
5. R. Courant and D. Hilbert, "Methods of Mathematical Physics," Vol. I, Wiley, New York, 1953.
6. A. Dutt, M. Gu, and V. Rokhlin, "Fast Algorithms for Polynomial Interpolation, Integration and Differentiation," Research Report YALEU/DCS/RR-997, July 1993.
7. A. Greenbaum, L. Greengard, and G. B. McFadden, Laplace's equation and the Dirichlet-Neumann map in multiply connected domains, J. Comput. Phys. 105, No. 2 (1993).
8. L. Greengard and V. Rokhlin, A fast algorithm for particle simulations, J. Comput. Phys. 73 (1987), 325-348.
9. L. Greengard and M. Moura, On the numerical evaluation of electrostatic fields in composite materials, Acta Numer. (1994), 379-410.
10. G. Golub and F. Van Loan, "Matrix Computation," Johns Hopkins Univ. Press, Baltimore/London, 1989.
11. P. Henrici, Applied and Computational Complex Analysis, Vol. III, Wiley New York, 1986.
12. G. C. Hsiao, P. Kopp, and W. L. Wendland, Some applications of a Galerkin collocation method for integral equations of the first kind, Math. Methods Appl. Sci. 6 (1984), 280-325.
13. S. Kapur and V. Rokhlin, "High-Order Corrected Trapezoidal Quadrature Rules for Singular Functions," Technical Report 1042, Yale University, Department of Computer Science, 1994.
14. N. Kerzman and R. Stein, The Cauchy kernel, the Szego kernel, and the Riemann mapping function, Math. Ann. 236 (1978), 85-93.
15. P. Koosis, "The Logarithmic Integral," Vol. 2, Cambridge Univ. Press, Cambridge, 1988.
16. R. Kress, "Linear Integral Equations," Springer-Verlag, Berlin, 1989.
17. S. O'Donnell and V. Rokhlin, A fast algorithm for the numerical evaluation of conformai mappings, SIAM J. Sci. Stat. Comput. 10, No. 3 (1989).
18. L. Reichel, On polynomial approximation in the complex plane with application to conformal mapping, Math. Comp. 44 (1985), 425-433.
19. L. Reichel, A fast method for sloving certain integral equations of the first kind with application to conformal mapping, J. Comput. Appl. Math. 14 (1986), 125-142.
20. V. Rokhlin, Rapid solution of integral equations of classical potential theory, J. Comput. Phys. 60 (1985), 187-207.
21. V. Rokhlin, End-point corrected trapezoidal quadrature rules for singular functions, Computers Math. Appl. 20, No. 7 (1990), 51-62.
22. J. Stoer and R. Bulirsch, "Introduction to Numerical Analysis," Springer-Verlag, New York/Berlin, 1983.
23. L. N. Trefethen (Ed.), "Numerical Conformal Mapping," North-Holland, Amsterdam, 1986. [Also available as Vol. 14 (1986), J. Comput. Appl. Math.]
24. L. N. Trefethen (Ed.), "Numerical Conformal Mapping," North-Holland, Amsterdam, 1986. [Also available as Vol. 14 (1986), J. Comput. Appl. Math.]
25. D. Yu and G. Tryggvason, The free-surface signature of unsteady two-dimensional vortex flows, J. Fluid Mech. 218 (1990), 547-572.
26. J. L. Walsh, "Interpolation and Approximation by Rational Functions in the Complex Domain," Colloq. Publ., Vol. 20, Amer. Math. Soc., Providence, RI, 1935.