Approximation Techniques for Engineers

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