Classical and Modern Numerical Analysis Theory, Methods and Practice [Hardcover]

Classical and Modern Numerical Analysis: Theory, Methods and Practiceprovides a sound foundation in numerical analysis for more specialized topics, such as finite element theory, advanced numerical linear algebra, and optimization. It prepares graduate students for taking doctoral examinations in numerical analysis.

The text covers the main areas of introductory numerical analysis, including the solution of nonlinear equations, numerical linear algebra, ordinary differential equations, approximation theory, numerical integration, and boundary value problems. Focusing on interval computing in numerical analysis, it explains interval arithmetic, interval computation, and interval algorithms. The authors illustrate the concepts with many examples as well as analytical and computational exercises at the end of each chapter.

This advanced, graduate-level introduction to the theory and methods of numerical analysis supplies the necessary background in numerical methods so that students can apply the techniques and understand the mathematical literature in this area. Although the book is independent of a specific computer program, MATLAB^?code is available on the authors' website to illustrate various concepts.

Mathematical Review and Computer Arithmetic

Mathematical Review

Computer Arithmetic

Interval Computations

Numerical Solution of Nonlinear Equations of One Variable

Introduction

Bisection Method

The Fixed Point Method

Newtons Method (NewtonRaphson Method)

The Univariate Interval Newton Method

Secant Method and M?llers Method

Aitken Acceleration and Steffensens Method

Roots of Polynomials

Additional Notes and Summary

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