Syllabus
Best approximation in normed linear spaces, approximation operators. Polynomial approximation: Barycentric interpolation formula, Chebyshev interpolant and projection.
Minimax approximation, Haar condition, Remez algorithm. Least squares approximation, orthogonal polynomials, periodic functions, uniform convergence, Jackson's theorems.
Practical applications: Chebfun, spectral methods, matrix functions.
Annotation
Introduction to approximation theory of continuous functions in normed linear spaces, with an emphasis on numerical methods for the computation of approximations.
The course deals with problems of polynomial interpolation, minimax approximation, and least squares approximation. Students will test the algorithms practically during the exercise.