Approximation Techniques for Engineers

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