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Tuesday, May 19, 2020 | History

2 edition of Chebyshev series for mathematical functions. found in the catalog.

Chebyshev series for mathematical functions.

C. W. Clenshaw

Chebyshev series for mathematical functions.

by C. W. Clenshaw

  • 122 Want to read
  • 37 Currently reading

Published by H.M. Stationery Off. in London .
Written in English

    Subjects:
  • Chebyshev polynomials.

  • Edition Notes

    Bibliography: p. 16.

    SeriesTeddington, Eng., National Physical Laboratory. Mathematical tables -- v. 5., Mathematical tables (National Physical Laboratory (Great Britain)) -- v. 5.
    ContributionsNational Physical Laboratory (Great Britain)
    The Physical Object
    Paginationiv, 36 p.
    Number of Pages36
    ID Numbers
    Open LibraryOL16587900M

    M. Razaz and J. L. Schonfelder () Remark on Algorithm Airy functions using Chebyshev series approximations. ACM Trans. Math. Software 7 (3), pp. – () Chebyshev series solutions of Fredholm integral equations. International Journal of Mathematical Education in Science and Technology , () An algorithm for the evaluation of multidimensional (direct and inverse) discrete Chebyshev transforms.

    Mathematical function, suitable for both symbolic and numerical manipulation. Explicit polynomials are given for integer n.. For certain special arguments, ChebyshevT automatically evaluates to exact values. ChebyshevT can be evaluated to arbitrary numerical precision. ChebyshevT automatically threads over lists. The goal of this book is to teach spectral methods for solving boundary value, eigenvalue, and time-dependent problems. Although the title speaks only of Chebyshev polynomials and trigonometric functions, the book also discusses Hermite, Laguerre, rational Chebyshev, sinc, and spherical harmonic functions.

    We obtain the representation of the backward shift operator on Chebyshev polynomials involving a principal value (PV) integral. Twice the backward shift on the space of square-summable sequences. There are quite a number of excellent books on approximation theory. Three classics are [Cheney ], [Davis ], and [Meinardus ], and a slightly more recent computationally oriented classic is [Powell ]. Perhaps the first approximation theory text was [Borel ]. A good deal of my emphasis will be on ideas related to Chebyshev.


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Chebyshev series for mathematical functions by C. W. Clenshaw Download PDF EPUB FB2

This item: Chebyshev and Fourier Spectral Methods: Second Revised Edition (Dover Books on Mathematics) by John P. Boyd Paperback $ Only 12 left in stock (more on the way). Ships from and sold by by: Solving Transcendental Equations is unique in that it is the first book to describe the Chebyshev-proxy rootfinder, which is the most reliable way to find all zeros of a smooth function on the interval, and the very reliable spectrally enhanced Weyl bisection/marching triangles method for bivariate rootfinding.

It also includes three chapters on analytical methods - explicit solutions, regular pertubation expansions, and singular perturbation series Cited by:   Combinatorics and Discrete Mathematics Book: Elementary Chebyshev series for mathematical functions.

book Theory (Raji) 7: Introduction to Analytic Number Theory Expand/collapse global location We define also the following functions, the last two functions are called Chebyshev’s functions. \(\pi(x)=\sum_{p\leq x}1.\).

Chebyshev series is efficiently solved by means of Clenshaw’s method, which is also pre-sented in this chapter. Before this, we give a very concise overview of well-known results in interpola-tion theory, followed by a brief summary of important properties satisfied by Chebyshev polynomials.

Basic results on interpolation Consider a real function fthat is continuous on the real interval [a,b]. When File Size: KB. Chebyshev polynomials form a special class of polynomials whose properties make them especially suited for approximating other functions.

As such, they form an essential part of any numerical library. The Extreme Optimization Numerical Libraries supports Chebyshev series through the ChebyshevSeries class. Chebyshev Series Approximations for the Bessel Function Y n (z) of Complex Argument by Jun Zhang, John A.

Belward - Appl. Math. Comput, We employ the truncated Chebyshev series to approximate the Bessel function of the second kind Yn (z) for jzj 8. Far from being an esoteric subject, Chebyshev polynomials lead one on a journey through all areas of numerical analysis. This book is the ideal vehicle with which to 5/5(3).

"The book presents a wide panorama of the applications of Chebyshev polynomials to scientific computing. [It] is very clearly written and is a pleasure to read. Examples inserted in the text allow one to test his or her ability to understand and use the methods, which are described in detail, and each chapter ends with a section full of very.

The Chebyshev series converges to f(x) if the function is piecewise smooth and continuous. The smoothness requirement can be relaxed in most cases — as long as there are a finite number of discontinuities in f (x) and its derivatives.

The Dynamic Dictionary of Mathematical Functions (DDMF) 39 First terms and polynomial approximation: order = The coefficients in the satisfy the recurrence Approximations by successive truncations of the Chebyshev series on -2 Errors of approximation by successive truncations of the Chebyshev series on -1 8.

Laplace. The basic idea is to use an encoding of a mathematical function by a series of coe cients corresponding to an expansion in orthonormal polynomials (Chebyshev series or for brevity, CS), and compute with that sequence of coe cients as an approximate model for the function.

The concept is probably comfortable to. Get this from a library. Chebyshev series for mathematical functions. This work is composed of 14 chapters that cover the machinery for the expansion of the generalized hypergeometric function and other functions in infinite series of Jacobi and Chebyshev polynomials of the first kind.

Numerical coefficients for Chebyshev expansions of the more common functions. Additional Physical Format: Online version: Clenshaw, C.W.

Chebyshev series for mathematical functions. London: H.M. Stationery Off., (OCoLC) Mathematical Functions and their Approximations is an updated version of the Applied Mathematics Series 55 Handbook based on the Conference on Mathematical Tables, held at Cambridge, Massachusetts.

The aim of the conference is to determine the need for mathematical tables in view of the availability of high speed computing machinery.

Chebyshev series and interpolants. Chebfun is founded on the mathematical subject of approximation theory, and in particular, on Chebyshev series and interpolants.

Conversely, it provides a simple environment in which to demonstrate these approximants and other approximation ideas. CLENSHAW, C.W Chebyshev series for mathematical functions. In Mathematical Tables, vol.

5, National Physical Laboratory, Her Majesty's Statmnery Office, London, England, The subject of the book is the approximation of functions of one or more variables by means of more elementary functions, regarded as a tool in numerical computation. It discusses the systems of trigonometric sums, rational functions, continued fractions, and spline functions.

These systems may be divided into linear and nonlinear. The Chebyshev series expansion may be seen as a cosine Fourier series, so that it possesses the valuable properties of the latter concerning, in particular, the convergence and the possible use of the FFT.

On the other hand, the Chebyshev series expansion is. CELEFUNT: A portable test package for complex elementary functions, ACM Trans. Math. Software 19 (), CP66 C. Clenshaw and S. Picken, Chebyshev series for Bessel functions of fractional order, National Physical Laboratory Mathematical Tables, vol.

8, Her Majesty's Stationery Office, London, CW. Solving Transcendental Equations is unique in that it is the first book to describe the Chebyshev-proxy rootfinder, which is the most reliable way to find all zeros of a smooth function on the interval, and the very reliable spectrally enhanced Weyl bisection/marching triangles method for bivariate rootfinding.Exact Chebyshev expansion coefficients of a function we shall compare the results of the Chebfun construction process to a known closed-form formula for the Chebyshev expansion coefficients of a function with a pole.

The evaluation and estimation of the coefficients in the Chebyshev series expansion of a function, Mathematics of.In the present third volume the reader will find: 1. An essay on the development of Chebyshev's theory of approximation of functions, later called "constructive function theory" by S.

N. Bernshtein. This highly original essay is due to the late N. I. Akhiezer (), the author of .