Approximation Theory

From Taylor Polynomials to Wavelets

Author: Ole Christensen,Khadija Laghrida Christensen

Publisher: Springer Science & Business Media

ISBN: 0817644482

Category: Mathematics

Page: 156

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This concisely written book gives an elementary introduction to a classical area of mathematics – approximation theory – in a way that naturally leads to the modern field of wavelets. The exposition, driven by ideas rather than technical details and proofs, demonstrates the dynamic nature of mathematics and the influence of classical disciplines on many areas of modern mathematics and applications. Featuring classical, illustrative examples and constructions, exercises, and a discussion of the role of wavelets to areas such as digital signal processing and data compression, the book is one of the few to describe wavelets in words rather than mathematical symbols.
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Scientific Computing

An Introductory Survey, Revised Second Edition

Author: Michael T. Heath

Publisher: SIAM

ISBN: 1611975573

Category: Science

Page: 567

View: 321

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This book differs from traditional numerical analysis texts in that it focuses on the motivation and ideas behind the algorithms presented rather than on detailed analyses of them. It presents a broad overview of methods and software for solving mathematical problems arising in computational modeling and data analysis, including proper problem formulation, selection of effective solution algorithms, and interpretation of results.? In the 20 years since its original publication, the modern, fundamental perspective of this book has aged well, and it continues to be used in the classroom. This Classics edition has been updated to include pointers to Python software and the Chebfun package, expansions on barycentric formulation for Lagrange polynomial interpretation and stochastic methods, and the availability of about 100 interactive educational modules that dynamically illustrate the concepts and algorithms in the book. Scientific Computing: An Introductory Survey, Second Edition is intended as both a textbook and a reference for computationally oriented disciplines that need to solve mathematical problems.
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Approximation Theory

In Memory of A.K. Varma

Author: Narenda Govil,Ram N. Mohapatra,Zuhair Nashed,A. Sharma,J. Szabados

Publisher: CRC Press

ISBN: 9780824701857

Category: Mathematics

Page: 552

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"Contains the contributions of 45 internationally distinguished mathematicians covering all areas of approximation theory-written in honor of the pioneering work of Arun K. Varma to the fields of interpolation and approximation of functions, including Birhoff interpolation and approximation by spline functions."
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Time‒Frequency and Time‒Scale Methods

Adaptive Decompositions, Uncertainty Principles, and Sampling

Author: Jeffrey A. Hogan

Publisher: Springer Science & Business Media

ISBN: 9780817644314

Category: Mathematics

Page: 390

View: 2671

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Developed in this book are several deep connections between time-frequency (Fourier/Gabor) analysis and time-scale (wavelet) analysis, emphasizing the powerful adaptive methods that emerge when separate techniques from each area are properly assembled in a larger context. While researchers at the forefront of these areas are well aware of the benefits of such a unified approach, there remains a knowledge gap in the larger community of practitioners about the precise strengths and limitations of Fourier/Gabor analysis versus wavelets. This book fills that gap by presenting the interface of time-frequency and time-scale methods as a rich area of work. "Foundations of Time-Frequency and Time-Scale Methods" will be suitable for applied mathematicians and engineers in signal/image processing and communication theory, as well as researchers and students in mathematical analysis, signal analysis, and mathematical physics.
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Fourier Analysis

Analytic and Geometric Aspects

Author: William O. Bray,P. Milojevic,C.V. Stanojevic

Publisher: CRC Press

ISBN: 9780824792084

Category: Mathematics

Page: 472

View: 9112

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Providing complete expository and research papers on the geometric and analytic aspects of Fourier analysis, this work discusses new approaches to classical problems in the theory of trigonometric series, singular integrals/pseudo-differential operators, Fourier analysis on various groups, numerical aspects of Fourier analysis and their applications, wavelets and more.
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Representations, Wavelets, and Frames

A Celebration of the Mathematical Work of Lawrence W. Baggett

Author: Palle E. T. Jorgensen,Kathy D. Merrill,Judith A. Packer

Publisher: Springer Science & Business Media

ISBN: 0817646833

Category: Mathematics

Page: 324

View: 5435

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The work of Lawrence Baggett has had a profound impact on the field of abstract harmonic analysis and the many areas of mathematics that use its techniques. His sphere of influence ranges from purely theoretical results regarding the representations of locally compact groups to recent applications of wavelets and frames to problems in sampling theory and image compression. Contributions in this volume reflect this broad scope, and Baggett’s unusual ability to bring together techniques from disparate fields. Recent applications to problems in sampling theory and image compression are included.
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