<p>This introduction to modern numerical methods encourages students in mathematics, physics, engineering, computer science or physical science to develop computational intuition and self-reliance by comparing the performance of various methods in solving a given problem. Number representation and round-off are presented in a hypothetical computer decimal word, instead of in binary representation, to simplify the explanation of origins and propagation of round-off error. Linear equations are studied directly after the general topics of round-off and error propagation. New optional sections include explanation and demonstration of Fourier and differential equation methods for analyzing linear systems in either state space or block diagram representations. Recent developments are reflected in material covering computational practice in an expanded eigenvalue section, and the discrete Fourier transform, with its application to filtering, is explained.</p>

An introduction to numerical computations

Science & Math

Yakowitz, Sidney J.

Mathematics

Collier/Macmillan

Computational Probability and Simulation (Addison-Wesley Series in Chemistry)

Addison-Wesley Publishing Company

It is an incontestable fact that numerical analysis techniques are used rou tinely (although not always effectively) in virtually every quantitative field of scientific endeavor. In this book, which is directed toward upper-division and graduate level students in engineering and mathematics, we have selected for discussion subjects that are traditionally found in numerical analysis texts. But our choice of methodology rejects the traditional where analysis and experience clearly warrant such a departure, and one of our primary aspirations in this work is to equip the reader with the wherewithal to apply numerical analysis thinking to nontraditional subjects. For there is a plethora of computer-oriented sciences such as optimization, statistics, and system analysis and identification that are sorely in need of methods comparable to those related here for classical numerical analysis problems. Toward uncovering for the reader the structure of numerical methods we have, for example, devoted a chapter to a metric space theory for iter ative application of operators. In this chapter, we have collected those definitions and concepts of real and functional analysis that are requisite to a modern intermediate-level exposition of the principles of numerical anal ysis. Further, we derive the abstract theory (most notably, the contraction mapping theorem) for iteration processes.

Principles and Procedures of Numerical Analysis (Mathematical Concepts and Methods in Science and Engineering, 14)

Szidarovszky, Ferenc

Springer

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