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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1985-0777274-0
PII: S 0025-5718(1985)0777274-0
Keywords: Polynomial approximation, polynomial basis, numerical condition, conformal mapping
Article copyright: © Copyright 1985 American Mathematical Society