- 240 pages
- English
- ePUB (mobile friendly)
- Available on iOS & Android
eBook - ePub
About this book
This concise text introduces numerical analysis as a practical, problem-solving discipline. The three-part presentation begins with the fundamentals of functional analysis and approximation theory. Part II outlines the major results of theoretical numerical analysis, reviewing product integration, approximate expansion methods, the minimization of functions, and related topics. Part III considers specific subjects that illustrate the power and usefulness of theoretical analysis.
Ideal as a text for a one-year graduate course, the book also offers engineers and scientists experienced in numerical computing a simple introduction to the major ideas of modern numerical analysis. Some practical experience with computational mathematics and the ability to relate this experience to new concepts is assumed. Otherwise, no background beyond advanced calculus is presupposed. Moreover, the ideas of functional analysis used throughout the text are introduced and developed only to the extent they are needed.
Ideal as a text for a one-year graduate course, the book also offers engineers and scientists experienced in numerical computing a simple introduction to the major ideas of modern numerical analysis. Some practical experience with computational mathematics and the ability to relate this experience to new concepts is assumed. Otherwise, no background beyond advanced calculus is presupposed. Moreover, the ideas of functional analysis used throughout the text are introduced and developed only to the extent they are needed.
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Yes, you can access Theoretical Numerical Analysis by Peter Linz in PDF and/or ePUB format, as well as other popular books in Mathematics & Mathematical Analysis. We have over one million books available in our catalogue for you to explore.
Information
PART I
BASIC CONCEPTS
Numerical analysis or, as it is perhaps more appropriately called, computational mathematics is the study of methods for the numerical (and, in general, approximate) solution of mathematically posed problems. Loosely speaking one can distinguish between two different aspects of computational mathematics: methodology, which deals with the construction of specific algorithms, their efficiency, implementation for computers, and various other practical questions, and analysis, in which one studies the underlying principles, error bounds, convergence theorems, and so on. It is this second aspect that is our main concern.
Most introductory treatments of numerical analysis stress methodology, and the student is exposed to a number of different algorithms which, on the surface, seem to have little in common. A deeper study, however, reveals a different picture. There are a few basic principles on which most of computational mathematics is based; often seemingly different methods are based on the same general idea. It is our aim to study these basic principles and to single out the fundamental notions which are the heart of modern numerical analysis. No attempt will be made to discuss particular problems or algorithms, except as examples for a general theory. To understand the principles on which numerical analysis is based is not only of interest to the mathematician, but can also be of considerable help in practical computation since a clear idea of the fundamentals is valuable in the construction of solution methods for the difficult problems encountered in practice.
We will begin by reviewing some simple results from functional analysis and approximation theory. A knowledge of these concepts is indispensable for further work; functional analysis provides us with a language for the development of a general theory, while approximation theory makes it possible to relate this theory to specific cases in a meaningful way. Both subjects are of course very extensive and contain topics of little use to the numerical analyst. Fortunately, the ideas needed here are the simpler ones, so that we need not delve into these subjects very deeply.
1
REVIEW OF FUNCTIONAL ANALYSIS
Modern numerical analysis has benefited considerably from its close association with functional analysis, which provides it not only with an elegant and concise notation, but also with an efficient tool for the development of new theories. Because of this, it is becoming increasingly more difficult for anyone unfamiliar with functional analysis to appreciate the current developments in numerical analysis. Fortunately, matters are not as difficult as they sometimes seem and it is not necessary to become an expert in functional analysis; what ...
Table of contents
- Cover
- Title Page
- Copyright Page
- Preface
- Contents
- Part I Basic Concepts
- Part II Theoretical Aspects of Computational Mathematics
- Part III Special Topics
- References
- Index