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 ...

SIAM Journal on Numerical Analysis, Vol. 52, No. 4 (2014), pp. 1913-1927 (15 pages) Polynomial interpolants defined using Chebyshev extreme points as nodes converge uniformly at a geometric rate when ...

Densities for the angle Θ = uX(mod 2π) and the cosine $Y = \cos(uX)$ can be expressed, through Fourier methods, in terms of the characteristic function of X. Thus ...

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 ...