Approximation Theory and Algorithms for Data Analysis

<p>This textbook offers an accessible introduction to the theory and numerics of approximation methods, combining classical topics of approximation with recent advances in mathematical signal processing, and adopting a constructive approach, in which the development of numerical algorithms for data analysis plays an important role.</p><p></p><p></p> <p>The following topics are covered:<br></p><p></p> <p>* least-squares approximation and regularization methods</p><p></p> <p>* interpolation by algebraic and trigonometric polynomials</p> <p>* basic results on best approximations</p> <p>* Euclidean approximation</p> <p>* Chebyshev approximation</p> <p>* asymptotic concepts: error estimates and convergence rates</p> <p>* signal approximation by Fourier and wavelet methods</p> <p>* kernel-based multivariate approximation</p> <p>* approximation methods in computerized tomography</p> <p>Providing numerous supporting examples, graphical illustrations, and carefully selected exercises, this textbook is suitable for introductory courses, seminars, and distance learning programs on approximation for undergraduate students.<br></p><p></p><br><p></p>