Principles and Procedures of Numerical Analysis

Description

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. Front Matter....Pages i-xii Preliminaries....Pages 1-24 Approximation and Interpolation of Functions....Pages 25-71 Numerical Differentiation and Integration....Pages 73-109 General Theory for Iteration Methods....Pages 111-140 Solution of Nonlinear Equations....Pages 141-178 The Solution of Simultaneous Linear Equations....Pages 179-220 The Solution of Matrix Eigenvalue Problems....Pages 221-256 The Numerical Solution of Ordinary Differential Equations....Pages 257-293 The Numerical Solution of Partial Differential Equations....Pages 295-319 Back Matter....Pages 321-331