Numerical Analysis Second Edition

Published 2006

Numerical Analysis is a text for students of engineering, science, mathematics, and computer science who have completed elementary calculus and matrix algebra. The primary goal is to construct and explore algorithms for solving science and engineering problems.

The not-so-secret secondary mission is to help the reader locate these algorithms in a landscape of some potent and far reaching principles. These unifying principles, taken together, constitute a dynamic field of current research and development in modern numerical and computational science.

The discipline of numerical analysis is jam-packed with useful ideas. Textbooks run the risk of presenting the subject as a bag of neat but unrelated tricks. For a deep understanding, readers need to learn much more than how to code Newton's Method, Runge-Kutta, and the Fast Fourier Transform. They must absorb the big principles, the ones that permeate numerical analysis and integrate its competing concerns of accuracy and efficiency.

The notions of convergence, complexity, conditioning, compression, and orthogonality are among the most important of the big ideas. Any approximation method worth its salt must converge to the correct answer as more computational resources are devoted to it, and the complexity of a method is a measure of its use of these resources. The conditioning of a problem, or susceptibility to error magnification, is fundamental to knowing how it can be attacked. Many of the newest applications of numerical analysis strive to realize data in a shorter or compressed way. Finally, orthogonality is crucial for efficiency in many algorithms, and is irreplaceable where conditioning is an issue or compression is a goal.

In this book, the roles of the five concepts in modern numerical analysis are emphasized in short thematic elements called Spotlights. They comment on the topic at hand and make informal connections to other expressions of the same concept elsewhere in the book. We hope that highlighting the five concepts in such an explicit way functions as a Greek chorus, accentuating what is really crucial about the theory on the page.

Although it is common knowledge that the ideas of numerical analysis are vital to the practice of modern science and engineering, it never hurts to be obvious. The Reality Checks provide concrete examples of the way numerical methods lead to solutions of important scientific and technological problems. These extended applications were chosen to be timely and close to everyday experience. Although it is impossible (and probably undesirable) to present the full details of the problems, the Reality Checks attempt to go deeply enough to show how a technique or algorithm can leverage a small amount of mathematics into a great payoff in technological design and function. The Reality Checks proved to be extremely popular as a source of student projects in the first edition, and have been extended and amplified in the second edition.

*Book is in excellent pre-loved condition.