ABSTRACT
This chapter deals with trigonometric interpolation. The two properties – automatic improvement of accuracy for smoother functions, and slow growth of the Lebesgue constants that translates into numerical stability – are distinctly different from the properties of algebraic interpolation on uniform grids. The chapter discusses Chebyshev polynomials and the relation between algebraic and trigonometric interpolation. It also discusses the problem of interpolation from the general perspective of approximation of functions by polynomials.
