Back Cover

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. The following topics are covered: * least-squares approximation and regularization methods * interpolation by algebraic and trigonometric polynomials * basic results on best approximations * Euclidean approximation * Chebyshev approximation * asymptotic concepts: error estimates and convergence rates * signal approximation by Fourier and wavelet methods * kernel-based multivariate approximation * approximation methods in computerized tomography 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.

Author Biography

Armin Iske is professor of numerical approximation at the Department of Mathematics of the University of Hamburg.

Table of Contents

1 Introduction.- 2 Basic Methods and Numerical Analysis.- 3 Best Approximations.- 4 Euclidean Approximations.- 5 Chebyshev Approximations.- 6 Asymptotic Results.- 7 Basic Concepts of Signal Approximation.- 8 Kernel-Based Approximation.- 9 Computational Topology.- References.- Subject Index.- Name Index.

Review

"This book is an excellent first course in approximation theory, covering all the aspects from theoretical results to practical methods, from discrete to continuous approximation, from univariate to multivariate. … The book is an excellent text for an undergraduate course in approximation methods. … this book is a very important textbook on approximation theory and its methods." (Ana Cristina Matos, Mathematical Reviews, August, 2019)

Review Quote

"This book is an excellent first course in approximation theory, covering all the aspects from theoretical results to practical methods, from discrete to continuous approximation, from univariate to multivariate. ... The book is an excellent text for an undergraduate course in approximation methods. ... this book is a very important textbook on approximation theory and its methods." (Ana Cristina Matos, Mathematical Reviews, August, 2019)

Feature

Clear and comprehensible introduction to approximation theory and its applications Offers a constructive approach to methods and algorithms Contains a large number of examples and exercises

Details