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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Approximation of complex harmonic functions by complex harmonic splines
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by Han Lin Chen and Tron Hvaring PDF
Math. Comp. 42 (1984), 151-164 Request permission

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.
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Additional Information
  • © Copyright 1984 American Mathematical Society
  • Journal: Math. Comp. 42 (1984), 151-164
  • MSC: Primary 30C30; Secondary 30E10, 41A15
  • DOI: https://doi.org/10.1090/S0025-5718-1984-0725990-8
  • MathSciNet review: 725990