Lectures on Constructive Approximation

Dr. Volker Michel teaches at University of Siegen

• Introduction: the Problem to be Solved.- Part I Basics.- Basic Fundamentals—What You Need to Know.- Approximation of Functions on the Real Line.- Part II Approximation on the Sphere.- Basic Aspects.- Fourier Analysis.- Spherical Splines.- Spherical Wavelet Analysis.- Spherical Slepian Functions.- Part III Approximation on the 3D Ball.- Orthonormal Bases.- Splines.- Wavelets for Inverse Problems on the 3D Ball.- The Regularized Functional Matching Pursuit (RFMP).- References.- Index.

From the book reviews: "This is a constructive approach to approximation by Fourier series (orthogonal polynomials), splines and wavelets. ... The basis functions are illustrated with many color plots and the proofs are fully written out. ... This is a clear introduction to subjects that are not easily found in other textbooks at this level. Obviously it is of interest for geophysical applications." (Adhemar Bultheel, zbMATH, Vol. 1295, 2014) "The textbook Lectures on constructive approximation teaches the basics and details of Fourier, spline, and wavelet methods on the real line, the sphere, and the ball. ... The style of the book is clearly that of a textbook, since the author makes a great effort to make very complicated concepts comprehensible to the reader. Throughout the book, numerous numerical examples and graphical illustrations support the explanations. This book is appropriate for applied mathematicians and numerical analysts as well as for geoscientists and engineers." (Willi Freeden, Mathematical Reviews, August, 2013)