This paper presents a generalization of the Remez multiple-exchange (ME) algorithm for solving complex Chebyshev approximation by polynomials on the unit circle. The difficulties of implementing the ...

Chebyshev polynomials, a central class of orthogonal polynomials, have long been pivotal in numerical analysis, approximation theory and the solution of differential equations. Their inherent ...

Kövari and Pommerenke [19], and Elliott [8], have shown that the truncated Faber series gives a polynomial approximation which (for practical values of the degree of the polynomial) is very close to ...

The implied volatility is a crucial element in any financial toolbox, since it is used to both quote and hedge options as well as for model calibration. In contrast to the Black–Scholes formula, its ...