Engineering Book from C.H.I.P.S.

Approximation Techniques for Engineers
by Louis Komzsik

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


  • 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


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


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Approximation Techniques for Engineers
by Louis Komzsik
2006 • 296 pages • $108.95 + shipping
Texas residents please add 6.75 % sales tax

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