An interior-point method for complex polynomial minimax

The package is to compute the polynomial minimax approximation for a continuous function or discrete case in the complex plane.

The purpose of this package is to compute the polynomial minimax approximation for a continuous function or discrete case in the complex plane.

The main function IntriorPt_VanvArld.m uses the interior-point method to solve the dual problem of the original minimax problem. The weights are the dual variables. The detailed procedure is given in

[1] L. Yang, L.-H. Zhang and Y. Zhang, The Lq-weighted dual programming of the linear Chebyshev approximation and an interior-point method, 2023, URL https://arxiv.org/ abs/2308.07636.

Run demo for testing.

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Dependence:

a. The method uses Vandermonde with Arnoldi (P. D. Brubeck and Y. Nakatsukasa and L. N. Trefethen, SIREV, 2021, Vol. 63, No. 2, pp. 405-415) to deal with the ill-conditioned Vandermonde basis, and also uses it to compute values of the minimax approximant at new nodes. The basic Arnoldi process is used in the fitting stage.

b. The package also contains Lawson’s iteration Lawson_VanvArld.m (C. L. Lawson, Contributions to the Theory of Linear Least Maximum Approximations, PhD thesis, UCLA, USA, 1961) for comparison.

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Reference:

[1] L. Yang, L.-H. Zhang and Y. Zhang, The Lq-weighted dual programming of the linear Chebyshev approximation and an interior-point method, 2023, URL https://arxiv.org/ abs/2308.07636.