Numerical Analysis

by Sauer, Timothy

• ISBN13: 9780321268983
• ISBN10: 0321268989
• Edition: 1st
• Format: Hardcover
• Copyright: 2005-12-07
• Publisher: Pearson

Summary

Numerical Analysis, designed to be used in a one-year course in engineering, science and mathematics, helps the readers gain a deeper understanding of numerical analysis by highlighting the five major ideas of the discipline: Convergence, Complexity, Conditioning, Compression, and Orthogonality and connecting back to them throughout the text. Each chapter contains a Reality Check, an extended foray into a relevant application area that can be used as a springboard for individual or team projects. MATLAB is used throughout to demonstrate and implement numerical methods. Fundamentals. Solving Equations. Systems of Equations. Interpolation. Least Square. Numerical Differentiation and Integration. Ordinary Differential Equations. Boundary Value Problems. Partial Differential Equations. Random Numbers and Applications. Trigonometric Interpolation and the FFT. Compression. Eigenvalues and Singular Values. Optimization. For all readers interested in numerical analysis.

Author Biography

Timothy Sauer earned the Ph.D. degree in mathematics at the University of California, Berkeley in 1982, and is currently a professor at George Mason University. He has published articles on a wide range of topics in applied mathematics, including dynamical systems, computational mathematics, and mathematical biology.

Table of Contents

Fundamentals

Evaluating a polynomial

Binary numbers

Decimal to binary

Binary to decimal

Floating point representation of real numbers

Floating point formats

Machine representation

Addition of floating point numbers

Loss of significance

Review of calculus

Software and Further Reading

Solving Equations

The Bisection Method

Bracketing a root

How accurate and how fast?

Fixed point iteration

Fixed points of a function

Geometry of Fixed Point Iteration

Linear Convergence of Fixed Point Iteration

Stopping criteria

Limits of accuracy

Forward and backward error

The Wilkinson polynomial

Sensitivity and error magnification

Newtonrsquo;s Method

Quadratic convergence of Newtonrsquo;s method

Linear convergence of Newtonrsquo;s method

Root-finding without derivatives

Secant method and variants

Brentrsquo;s Method

Kinematics of the Stewart platform

Software and Further Reading

Systems of Equations

Gaussian elimination

Naive Gaussian elimination

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