Numerical Analysis

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  • Edition: 1st
  • Format: Hardcover
  • Copyright: 2005-12-07
  • Publisher: Pearson
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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

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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