by Louis Komzsik
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