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Convergence of the Fraser-Hart algorithm for rational Chebyshev approximation


Author: Charles B. Dunham
Journal: Math. Comp. 29 (1975), 1078-1082
MSC: Primary 65D15
DOI: https://doi.org/10.1090/S0025-5718-1975-0388732-9
MathSciNet review: 0388732
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Abstract: The Fraser-Hart variant of the Remez algorithm is used to determine the best rational Chebyshev approximation to a continuous function on an interval. A necessary and sufficient condition for the matrix of the associated linear system to be nonsingular at the solution to the approximation problem is given. It is shown that the Fraser-Hart method may fail even if started arbitrarily close to the solution of the approximation problem. Use of the secant method in place of the Fraser-Hart iteration is also considered.


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DOI: https://doi.org/10.1090/S0025-5718-1975-0388732-9
Keywords: Chebyshev approximation, rational approximation, Fraser-Hart iteration
Article copyright: © Copyright 1975 American Mathematical Society

American Mathematical Society