Course Contents

Introduction to Approximation Theory, Solution of systems of equations: linear & nonlinear. Interpolation: Splines theory, B-Spline, Bezier curve, Chebyshev interpolation, Trigonometric interpolation. Approximation: Best approximations and orthogonal projections, Systems of orthogonal polynomials , The order of convergence of polynomial approximations, The uniform boundedness theorem, Finding best approximations, Existence and uniqueness of best approximations. Special Topics: Relation between interpolation and approximation, Collocation vs. Galerkin methods for differential equations, Proper orthogonal decomposition, Wavelet approximation, FFT transformation and their application Software: All computational examples will be presented using MATLAB.

Course Learning Outcomes

By the end of the course, students will have a firm knowledge of univariate and multivariate approximation theory, and apply these concepts in functional analysis, cagd, data science and scientific computing.