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

Reichel, Lothar

doi:10.1090/S0025-5718-1985-0777274-0

On polynomial approximation in the complex plane with application to conformal mapping
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Math. Comp. 44 (1985), 425-433 Request permission

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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