Filon

Filon can refer to multiple uses. In mathematics, Filon-type quadrature is a category of numerical methods designed to evaluate highly oscillatory integrals such as ∫_a^b f(x) e^{iωx} dx when the frequency ω is large. The core idea is to approximate the slowly varying function f(x) by a simple interpolant on subintervals and then integrate the product with the oscillatory factor exactly or analytically. This yields accurate results with relatively few function evaluations, avoiding the severe cancellation that afflicts standard quadrature for large ω. Over the years, many variants have been developed, including methods based on polynomial, spline, or Chebyshev interpolation, and adaptations to sine, cosine, or complex kernels.

Filon is also a surname, and it appears in various cultures. In non-mathematical contexts, Filon can refer to people, place names, or other uses depending on language and history.

Because of its mathematical significance, Filon-type quadrature is discussed in numerical analysis texts and research on computational methods for wave propagation, quantum mechanics, and signal processing.