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The Best Approximation Method An Introduction

  • Theodore V. HromadkaII
  • Chung-Cheng Yen
  • George F. Pinder

Part of the Lecture Notes in Engineering book series (LNENG, volume 27)

Table of contents

  1. Front Matter
    Pages N2-XIII
  2. Theodore V. Hromadka II, Chung-Cheng Yen, George F. Pinder
    Pages 1-17
  3. Theodore V. Hromadka II, Chung-Cheng Yen, George F. Pinder
    Pages 18-41
  4. Theodore V. Hromadka II, Chung-Cheng Yen, George F. Pinder
    Pages 42-49
  5. Theodore V. Hromadka II, Chung-Cheng Yen, George F. Pinder
    Pages 50-56
  6. Theodore V. Hromadka II, Chung-Cheng Yen, George F. Pinder
    Pages 57-80
  7. Theodore V. Hromadka II, Chung-Cheng Yen, George F. Pinder
    Pages 81-114
  8. Theodore V. Hromadka II, Chung-Cheng Yen, George F. Pinder
    Pages 115-161
  9. Back Matter
    Pages 162-171

About this book

Introduction

The most commonly used numerical techniques in solving engineering and mathematical models are the Finite Element, Finite Difference, and Boundary Element Methods. As computer capabilities continue to impro':e in speed, memory size and access speed, and lower costs, the use of more accurate but computationally expensive numerical techniques will become attractive to the practicing engineer. This book presents an introduction to a new approximation method based on a generalized Fourier series expansion of a linear operator equation. Because many engineering problems such as the multi­ dimensional Laplace and Poisson equations, the diffusion equation, and many integral equations are linear operator equations, this new approximation technique will be of interest to practicing engineers. Because a generalized Fourier series is used to develop the approxi­ mator, a "best approximation" is achieved in the "least-squares" sense; hence the name, the Best Approximation Method. This book guides the reader through several mathematics topics which are pertinent to the development of the theory employed by the Best Approximation Method. Working spaces such as metric spaces and Banach spaces are explained in readable terms. Integration theory in the Lebesque sense is covered carefully. Because the generalized Fourier series utilizes Lebesque integration concepts, the integra­ tion theory is covered through the topic of converging sequences of functions with respect to measure, in the mean (Lp), almost uniformly IV and almost everywhere. Generalized Fourier theory and linear operator theory are treated in Chapters 3 and 4.

Keywords

finite element method integral equation operator operator theory

Authors and affiliations

  • Theodore V. HromadkaII
    • 1
  • Chung-Cheng Yen
    • 2
  • George F. Pinder
    • 3
  1. 1.Department of MathematicsFullertonUSA
  2. 2.Williamson and SchmidIrvineUSA
  3. 3.Department of Civil EngineeringPrinceton UniversityPrincetonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-83038-9
  • Copyright Information Springer-Verlag Berlin Heidelberg 1987
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-17572-8
  • Online ISBN 978-3-642-83038-9
  • Series Print ISSN 0176-5035
  • Buy this book on publisher's site
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