Convergence of the Fraser-Hart algorithm for rational Chebyshev approximation

Dunham, Charles B.

doi:10.1090/S0025-5718-1975-0388732-9

Convergence of the Fraser-Hart algorithm for rational Chebyshev approximation
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by Charles B. Dunham PDF

Math. Comp. 29 (1975), 1078-1082 Request permission

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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