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Approximation techniques for engineers

Author: Louis Komzsik
Publisher: Boca Raton, FL : CRC/Taylor & Francis, ©2007.
Edition/Format:   eBook : Document : EnglishView all editions and formats

Describes major techniques that are available for obtaining approximate solutions for problems arising in engineering. This book examines the various methods for obtaining approximate solutions for  Read more...


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Genre/Form: Electronic books
Additional Physical Format: Print version:
Komzsik, Louis.
Approximation techniques for engineers.
Boca Raton, FL : CRC/Taylor & Francis, ©2007
(DLC) 2006040582
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Louis Komzsik
ISBN: 9781420009149 1420009141 1351792725 9781351792721
OCLC Number: 644989602
Reproduction Notes: Electronic reproduction. [S.l.] : HathiTrust Digital Library, 2010. MiAaHDL
Description: 1 online resource (xvii, 296 pages) : illustrations
Details: Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.
Contents: DATA APPROXIMATIONSClassical Interpolation Methods. Newton Interpolation. Lagrange Interpolation. Hermite Interpolation. Interpolation of Functions of Two Variables with Polynomials. ReferencesApproximation with Splines. Natural Cubic Splines. Bezier Splines. Approximations with B-Splines. Surface Spline Approximation. ReferencesLeast 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. ReferencesApproximation of Functions. Least Squares Approximation of Functions. Approximation with Legendre Polynomials. Chebyshev Approximation. Fourier Approximation. Pade Approximation. ReferencesNumerical Differentiation. Finite Difference Formulae. Higher Order Derivatives. Richardson's Extrapolation. Multipoint Finite Difference Formulae. ReferencesNumerical Integration. The Newton-Cotes Class. Advanced Newton-Cotes Methods. Gaussian Quadrature. Integration of Functions of Multiple Variables. Chebyshev Quadrature. Numerical Integration of Periodic Functions. ReferencesAPPROXIMATE SOLUTIONSNonlinear Equations in One Variable. General Equations. Newton's Method. Solution of Algebraic Equations. Aitken's Acceleration. ReferencesSystems 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. ReferencesIterative 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. ReferencesApproximate 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. ReferencesInitial 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. ReferencesBoundary 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. ReferencesClosing RemarksIndex
Responsibility: Louis Komzsik.


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"This book is meant as a reference book for engineers and graduate students. The goal is to give a working knowledge of various approximation techniques of engineering practice. Therefore, many parts Read more...

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