Chebyshev polynomials in the complex plane and generalizations of the Remez Algorithm.

I will discuss Chebyshev polynomials in the complex plane, which generalize Chebyshev polynomials on the real line. On subsets of the real line the classical Remez algorithm is useful in determining good approximations for the corresponding Chebyshev polynomials. The algorithm is based on the concept of an alternating set which does not exist for general complex Chebyshev polynomials. Generalizations of the Remez algorithm do however exist and I will discuss one of these proposed by Peter Tang[1] and then further studied by Bernd Fischer and Jan Modersitzki[2].

Presenter: Olof Rubin

[1]Tang, Ping. (1988). A Fast Algorithm for Linear Complex Chebyshev Approximations. Mathematics of Computation - Math. Comput.. 51. 721-721. 10.1090/S0025-5718-1988-0935074-5.

[2]Fischer, Bernd & Modersitzki, J.. (1993). An algorithm for complex linear approximation based on semi-in nite programming. Numerical Algorithms. 5. 287-297. 10.1007/BF02108463.