NUMERICAL METHODS III – APPROXIMATION OF FUNCTIONS

Sažetak:

Format: Colour on White Paper, 6.30″x8.86″ (225×160 mm), Paperback, 260 pages.

Several other Colour and Black & White options are also available.

An Black and White option can be found here .

About the book:

An excellent textbook established at several universities. Primarily written for students at technical universities, it is also a very useful handbook for engineers, PhD students and scientists. Now available in several forms at all continents.

This textbook introduces the reader into various types of approximations of functions, which are defined either explicitly or by their values in the distinct set of points, as well as into the economisation of existing approximation formulas.

Why the approximation of functions is so important? Simply, various functions (such as trigonometric functions and logarithms) cannot be calculated without approximation. Approximation formulas for some of these functions are already implemented in calculators and standard computer libraries, providing accuracy to all the bits in which a value is stored. High accuracy is usually not required and requires more numerical operations then necessary. Economised approximation formulas can provide the required accuracy with less numerical operations, and can make numerical algorithms faster, especially when such formulas are nested in loops. The other important use of approximation is in calculating functions that are defined by values at a chosen set of points.

The book is divided into five chapters. The first chapter briefly explains Maclaurin, Taylor or Padé expansion, principles of approximations with orthogonal series and principles of the least squares approximations.

In the second chapter, various types of least squares polynomial approximations, particularly those using Legendre, Jacobi, Laguerre, Hermite, Zernike and Gram orthogonal polynomials are explained. The third chapter explains approximations with Fourier series, which are the base for developing approximations with Chebyshev polynomials (fourth chapter).

Uniform approximation and further usage of Chebyshev polynomials in the almost uniform approximation, as well as in the economisation of the existing approximation formulas, are described in the fifth chapter.

Practical application of the described approximation procedures is supported by 40 examples and 37 algorithms. In addition to its practical usage, the given text with 37 figures and 12 tables represents a valuable background for understanding, using, developing and applying various numerical methods, such as interpolation, numerical integration and solving partial differential equations, which are topics covered in the following volumes of the series Numerical Methods.

Reviewed by:

Prof. Maja Fošner, D.Sc., University of Maribor, Slovenia

Prof. Damir Jelaska, D.Sc., University of Split, Croatia

Prof. Valery Lysenko, D.Sc., Academic of the Russian Metrological Academy, Russian Research Institute for Metrological Service, Russia

Prof. Iztok Potrč, D.Sc., University of Maribor, Slovenia

Prof. Evgeny Pushkar, D.Sc., Member correspondent of the Russian Academy of Natural Sciences, Moscow State Industrial University, Russia

Proof reading by:

Jasenka Topličanec, prof., Zagreb, Croatia

Bilješka o autoru: 

Boris Obsieger, D.Sc., professor at the University of Rijeka, Croatia. Head of Section for Machine Elements at the Faculty of Engineering in Rijeka. Holds lectures on Machine Elements Design, Robot Elements Design, Numerical Methods in Design and Boundary Element Method. Several invited lectures. President of CADAM Conferences. Main editor of international journal Advanced Engineering. Author of several books and a lot of scientific papers.

Ključne riječi: Least squares, Orthogonal polynomials, Fourier series expansion, Uniform approximation, Chebyshev economisation

Link: http://university-books.eu
E-mail: Boris Obsieger 1 , Boris Obsieger 2

Naslov: Numerical Methods III – Approximation of Functions (unutrašnjost crno-bijela)
Autor: Boris Obsieger
Broj stranica: 260
Nakladnik: Boris Obsieger
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