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 ...

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 ...

A new method for interpolation by rational functions of prescribed numerator and denominator degrees is presented. When the interpolation nodes are roots of unity or Chebyshev points, the algorithm is ...

Approximation theory and asymptotic methods form a foundational framework that bridges classical ideas with modern numerical analysis, enabling researchers to obtain practical, near‐optimal solutions ...