Introduction to Precise Numerical Methods

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Academic Press, Apr 11, 2007 - Mathematics - 272 pages
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Precise numerical analysis may be defined as the study of computer methods for solving mathematical problems either exactly or to prescribed accuracy. This book explains how precise numerical analysis is constructed. The book also provides exercises which illustrate points from the text and references for the methods presented.

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· Clearer, simpler descriptions and explanations of
the various numerical methods
· Two new types of numerical problems; accurately
solving partial differential equations with the included software and computing line integrals in the complex plane.
 

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Contents

1 Introduction
1
2 Computer Arithmetics
9
3 Classification of Numerical Computation Problems
25
4 RealValued Functions
37
5 Computing Derivatives
41
6 Computing Integrals
57
7 Finding Where a Function fx is Zero
69
8 Finding Roots of Polynomials
79
10 Eigenvalue and Eigenvector Problems
109
11 Problems of Linear Programming
137
12 Finding Where Several Functions are Zero
159
13 Optimization Problems
181
14 Ordinary Differential Equations
191
15 Partial Differential Equations
217
16 Numerical Methods with Complex Functions
235
Index
249

9 Solving n Linear Equations in n Unknowns
97

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About the author (2007)

Oliver Aberth received his B.S. from City College of New York, his M.S. from Massachusetts Institute of Technology, and his Ph.D. from the University of Pennsylvania. He is also the author of Computable Analysis (McGraw-Hill, 1980) and Precise Numerical Methods Using C++ (Academic Press, 1998). He was professor of mathematics at Texas A & M University from 1970 to 1999. He is currently professor emeritus at Texas A & M University.

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