On polynomial approximation in the complex plane with application to conformal mapping

Author:
Lothar Reichel

Journal:
Math. Comp. **44** (1985), 425-433

MSC:
Primary 30E10; Secondary 30C30, 41A10

DOI:
https://doi.org/10.1090/S0025-5718-1985-0777274-0

MathSciNet review:
777274

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Abstract: We consider the selection of polynomial bases for polynomial approximation of analytic functions on bounded simply connected regions in the complex plane. While a monomial basis may be very ill-conditioned, we show that a basis of Lagrange polynomials with Fejér points as nodes is well-conditioned. Numerical examples, where we compute polynomial approximations of conformal mappings, conclude the paper.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1985-0777274-0

Keywords:
Polynomial approximation,
polynomial basis,
numerical condition,
conformal mapping

Article copyright:
© Copyright 1985
American Mathematical Society