10 Best Books on Approximation Theory

“An Introduction to the Approximation of Functions” Book Review: The book provides an introduction to the needs of automatic digital computation with particular emphasis on approximation by polynomials. The book discusses the concepts of approximation theory with at least one algorithm leading to actual numerical approximation. The contents of the book will be useful for introductory courses in both mathematical and numerical analysis. It covers a variety of approximation methods, including interpolation methods and an introduction to splines. The book includes a knowledge of advanced calculus and linear algebra and is written for upper-level graduate students. At the end of each chapter there are exercises for students to practise and an excellent bibliography.

“Approximation Theory: From Taylor Polynomials to Wavelets” Book Review: This book gives an introduction to a classical area of mathematics, approximation theory, in a way that naturally leads to the modern field of wavelets. It also tells us how to do approximation using polynomials. It introduces us to an infinite series, with emphasis on approximation-theoretic aspects. Topics like Fourier analysis, elementary calculus and discussion of the role of wavelets in digital signal processing and data compression are all included in the book. It is an ideal book for students and instructors in pure and applied mathematics, mathematical physics and engineering.

“A Course In Approximation Theory” Book Review: The aim of the book is to explore contemporary approximation theory. Special attention is paid on the concept of multivariable approximation theory. The topics in the book contain concepts from basic knowledge to the current active research. The book contains practical problems arising in diverse applications such as science, engineering, geophysics and business and economics. The book consists of topics like projections, interpolation paradigms, positive definite functions, interpolation theorems of Schoenberg and Micchelli, etc. The book includes 438 problems and exercises for the reader to get a better understanding of the subject. The most important part of the book is bibliography of almost 600 items.

“Interpolation and Approximation by Polynomials (CMS Books in Mathematics)” Book Review: The contents of the book are about multivariate interpolation and multivariate numerical integration, a generalization of the Bernstein polynomials. The book covers the concept of Peano kernel theorem. The book includes many worked examples and each section ends with a number of carefully selected problems for the better understanding of students.

“The Design of Approximation Algorithms” Book Review: This book is a valuable resource for anyone seeking to learn how to design approximation algorithms that can find solutions that are nearly optimal, while also providing provable guarantees. The material covers essential algorithmic techniques for designing approximation algorithms, including greedy and local search algorithms, dynamic programming, and more. Each chapter in the first section focuses on a single algorithmic technique applied to various problems, with a more in-depth exploration of these techniques in the second section. The book also includes information on methods that can be used to prove that optimization problems are difficult to approximate. While it is primarily written for graduate-level algorithm courses, this book also serves as a useful reference for researchers interested in heuristic solutions to discrete optimization problems.

“Convergence Estimates in Approximation Theory” Book Review: This book mainly deals with the study of linear positive operators with significant relevance to studies of computer-aided geometric design, numerical analysis and differential equations. The focus of the book is on the convergence of linear positive operators in real and complex domains. The book explores new and more efficient methods of applying this research to studies in Optimization and Analysis. This will be a useful guide for upper-level students who are interested in this field and to researchers developing innovative approaches.

“Fundamentals of Approximation Theory” Book Review: This book represents a systematic, in-depth treatment of some basic topics in approximation theory designed to emphasize the rich connections of the subject with other areas of study. This book has a smooth approach from the very concrete to more and more abstract levels, this text provides an outstanding blend of classical and abstract topics. The theory is presented in such a way that readers need to begin research in this domain for better understanding. It covers some core topics like spline functions, orthogonal polynomials, approximation in normed linear spaces and expose readers to the use of complex analytic methods in approximation theory. In this book each chapter contains problems of varying difficulty, including some drawn from contemporary research. This book is for introductory graduate-level class, Fundamentals of Approximation Theory also contains enough advanced material to serve more specialized courses at the doctoral level and to interest scientists and engineers.