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 ...

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 ...

We address a more general version of a classic question in probability theory. Suppose X ∼ ${\bf N}_{{\bf p}}(\mu,\Sigma)$ (μ, Σ). What functions of X also have ...

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 ...