A Theoretical Introduction to Numerical Analysis

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CRC Press, Nov 2, 2006 - Mathematics - 552 pages
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A Theoretical Introduction to Numerical Analysis presents the general methodology and principles of numerical analysis, illustrating these concepts using numerical methods from real analysis, linear algebra, and differential equations. The book focuses on how to efficiently represent mathematical models for computer-based study.

An accessible yet rigorous mathematical introduction, this book provides a pedagogical account of the fundamentals of numerical analysis. The authors thoroughly explain basic concepts, such as discretization, error, efficiency, complexity, numerical stability, consistency, and convergence. The text also addresses more complex topics like intrinsic error limits and the effect of smoothness on the accuracy of approximation in the context of Chebyshev interpolation, Gaussian quadratures, and spectral methods for differential equations. Another advanced subject discussed, the method of difference potentials, employs discrete analogues of Calderon’s potentials and boundary projection operators. The authors often delineate various techniques through exercises that require further theoretical study or computer implementation.

By lucidly presenting the central mathematical concepts of numerical methods, A Theoretical Introduction to Numerical Analysis provides a foundational link to more specialized computational work in fluid dynamics, acoustics, and electromagnetism.

 

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This book is superb in terms of simplicity and elegance. The contents are well-written and well-organized. However, it is not a book for beginners. This book is the next step to Introductory Methods of Numerical Analysis by S.S. Sastry. Overall, this book is very good for the students who wants insight into strengths and limitations of a particular numerical method.  

Contents

Interpolation of Functions Quadratures
21
Trigonometric Interpolation
61
polants
80
Computation of Definite Integrals Quadratures
91
Direct Methods
119
Iterative Methods for Solving Linear Systems
173
Overdetermined Linear Systems The Method of Least Squares
211
i
445
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Page 514 - RB, Oden, JT, and Wellford, Jr., LC, 'A Finite Element Analysis of Shocks and Finite-Amplitude Waves in One-Dimensional Hyperelastic Bodies at Finite Strain", Int.
Page 509 - K. Binder and DW Heermann, Monte Carlo Simulation in Statistical Physics: an Introduction (Springer, Berlin, 1988).

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