Approximation Techniques for Engineers presents numerous examples, algorithms, and industrial applications.

Features:

• Presents a broad collection of methods that provide an approximate result for engineering computations
• Discusses classical interpolation methods, spline interpolations, and least-square approximations
• Covers various approximations of functions as well as their numerical differentiation and integration
• Addresses linear and nonlinear equations and systems, eigenvalue problems, and initial- and boundary-value problems
• Emphasizes the logical thread and common principles of the approximation techniques

Contents

Classical Interpolation Methods

• Newton Interpolation
• Lagrange Interpolation
• Hermite Interpolation
• Interpolation of Functions of Two Variables with Polynomials

Approximation with Splines

• Natural Cubic Splines
• Bezier Splines
• Approximations with B-Splines
• Surface Spline Approximation

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

Approximation of Functions

• Least Squares Approximation of Functions
• Approximation with Legendre Polynomials
• Chebyshev Approximation
• Fourier Approximation
• Padé Approximation

Numerical Differentiation

• Finite Difference Formulae
• Higher Order Derivatives
• Richardson's Extrapolation
• Multipoint Finite Difference Formulae

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

Nonlinear Equations in One Variable

• General Equations
• Newton's Method
• Solution of Algebraic Equations
• Aitken's Acceleration

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

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

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

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

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

Index

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