3 Credits (3-0-0)
Interpolation : general problem, representation theorems, remainder theory, convergence of interpolatory processes. Approximation : best, uniform and least-squares, degree of approximation. Approximation of linear functionals : Optimal approximations in Hilbert spaces, roots and extremals : Convergence of Newton’s method in Banach spaces, minimizing functionals on normed linear spaces, applications to integral equations and control theory.
Splines : applications to computer-aided design.
Filters : linear, least-squares and Chebyshev.
Applications to signal processing.