Approximation Techniques for Engineers
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Summary
Presenting numerous examples, algorithms, and industrial applications, Approximation Techniques for Engineers is your complete guide to the major techniques used in modern engineering practice. Whether you need approximations for discrete data of continuous functions, or you're looking for approximate solutions to engineering problems, everything you need is nestled between the covers of this book. Now you can benefit from Louis Komzsik's years of industrial experience to gain a working knowledge of a vast array of approximation techniques through this complete and self-contained resource.
Table of Contents
DATA APPROXIMATIONS
Classical Interpolation Methods
. Newton Interpolation
. Lagrange Interpolation
. Hermite Interpolation
. Interpolation of Functions of Two Variables with Polynomials
. References
Approximation with Splines
. Natural Cubic Splines
. Bezier Splines
. Approximations with B-Splines
. Surface Spline Approximation
. References
Least Squares Approximation
. The Least Squares Principle
. Linear Least Squares Approximation
. Polynomial Least Squares Approximation
. Computational Example
. Exponential and Logarithmic Least Squares Approximations
. Nonlinear Least Squares Approximation
. Trigonometric Least Squares Approximation
. Directional Least Squares Approximation
. Weighted Least Squares Approximation
. References
Approximation of Functions
. Least Squares Approximation of Functions
. Approximation with Legendre Polynomials
. Chebyshev Approximation
. Fourier Approximation
. Padé Approximation
. References
Numerical Differentiation
. Finite Difference Formulae
. Higher Order Derivatives
. Richardson's Extrapolation
. Multipoint Finite Difference Formulae
. References
Numerical Integration
. The Newton-Cotes Class
. Advanced Newton-Cotes Methods
. Gaussian Quadrature
. Integration of Functions of Multiple Variables
. Chebyshev Quadrature
. Numerical Integration of Periodic Functions
. References
APPROXIMATE SOLUTIONS
Nonlinear Equations in One Variable
. General Equations
. Newton's Method
. Solution of Algebraic Equations
. Aitken's Acceleration
. References
Systems of Nonlinear Equations
. The Generalized Fixed Point Method
. The Method of Steepest Descent
. The Generalization of Newton's Method
. Quasi-Newton Method
. Nonlinear Static Analysis Application
. References
Iterative Solution of Linear Systems
. Iterative Solution of Linear Systems
. Splitting Methods
. Ritz-Galerkin Method
. Conjugate Gradient Method
. Preconditioning Techniques
. Biconjugate Gradient Method
. Least Squares Systems
. The Minimum Residual Approach
. Algebraic Multigrid Method
. Linear Static Analysis Application
. References
Approximate Solution of Eigenvalue Problems
. Classical Iterations
. The Rayleigh-Ritz Procedure
. The Lanczos Method
. The Solution of the Tridiagonal Eigenvalue Problem
. The Biorthogonal Lanczos Method
. The Arnoldi Method
. The Block Lanczos Method
. Normal Modes Analysis Application
. References
Initial Value Problems
. Solution of Initial Value Problems
. Single-Step Methods
. Multistep Methods
. Initial Value Problems of Ordinary Differential Equations
. Initial Value Problems of Higher Order Ordinary Differential Equations
. Transient Response Analysis Application
. References
Boundary Value Problems
. Boundary Value Problems of Ordinary Differential Equations
. The Finite Difference Method for Boundary Value Problems of Ordinary Differential Equations
. Boundary Value Problems of Partial Differential Equations
. The Finite Difference Method for Boundary Value Problems of Partial Differential Equations
. The Finite Element Method
. Finite Element Analysis of Three-Dimensional Continuum
. Fluid-Structure Interaction Application
. References
Closing Remarks
Index
Editorial Reviews
"In this outstanding book the author gives a concise mathematical description of engineering approximation methods along with small computational examples to illustrate the numerical approaches. For future studies a short list of references is also given in each chapter. … I highly recommend Dr. Komzsik's book."
- Ortwin Ohtmer, Department of Mechanical and Aerospace Engineering, California State University, Long Beach
"This book is a well written and thorough examination of the wide range of approximation techniques used by engineers. The author has accumulated tremendous experience in applying such techniques to industrial problems, and the reader can benefit greatly from the computational examples in this book. Whether the reader is a student taking a class or a practicing engineer learning alone, this book would greatly enhance the learning process."
- John Brauer, Ph.D., IEEE Fellow, Program Director of Applied Technology Center™, Milwaukee School of Engineering, Wisconsin
"An amazing compilation ... Comprehensive and rigorous. Well structured and clearly described. Expertly demonstrated with numerical and graphical examples. Completed with references to seminal works. Dr. Komzsik masterly arranged all important data set approximation methods and non-exact computational solution procedures in this book, and explained them in a style that can be easily understood by everyone familiar with the mathematical and computational basics."
-Imre Horváth, Design Engineering, Delft University of Technology, the Netherlands, and Editor-in-Chief, Computer Aided Design
"Approximation Techniques for Engineers serves as an excellent reference book either to find the solution for a particular engineering problem or to understand the computational techniques behind today's CAE and CAD systems. The various examples help the practicing engineer to comprehend the different approaches without going through lengthy derivations."
-Dietmar Göhlich, Product Manager, S-class Passenger Car Development, Daimler-Chrysler Corporation, Germany
