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Mathematics of Computation

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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
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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Keywords: Polynomial approximation, polynomial basis, numerical condition, conformal mapping
Article copyright: © Copyright 1985 American Mathematical Society

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