Approximation of complex harmonic functions by complex harmonic splines-Reference-Cited by-同舟云学术

Approximation of complex harmonic functions by complex harmonic splines

Published:1984 Issue:165 Volume:42 Page:151-164
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Chen Han Lin,Hvaring Tron

Abstract

In this paper, a class of complex harmonic spline functions (C.H.S.) are defined on the unit disc U. We use the C.H.S. to approximate the complex harmonic function on U, showing that C.H.S. may be represented by elementary functions. If the maximum step tends to zero and the mesh ratio is bounded, then C.H.S. converge uniformly to the interpolated function F on the closed disc Ū. If the interpolated function F is a conformal mapping, then the C.H.S. is a quasi-conformal mapping.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/1984-42-165/S0025-5718-1984-0725990-8/S0025-5718-1984-0725990-8.pdf

Reference12 articles.

1. Complex cubic splines;Ahlberg, J. H.;Trans. Amer. Math. Soc.,1967

2. Splines in the complex plane;Ahlberg, J. H.,1969

3. Chen Han-Lin, Complex Harmonic Splines, Interpolation and Approximation on the Unit Circle, Part II, Tech. Report, Math. and Comp. No. 3/81, ISBN 82-7151-039-8.

4. Complex spline functions;Chen, Han Lin;Sci. Sinica,1981

5. Chen Han-Lin & Tron Hvaring, A New Method for the Approximation of Conformal Mapping on the Unit Circle, Tech. Report, Math. and Comp. No. 6/82, ISBN 82-7151-049-5.

Cited by 3 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. References;Handbook of Splines;1999

2. Spline Wavelets on the Unit Circle;Results in Mathematics;1997-05

3. Properties of Complex Harmonic Splines;Numerical Functional Analysis and Optimization;1992-01