Chebyshev series for mathematical functions

  title={Chebyshev series for mathematical functions},
  author={C. W. Clenshaw},
Chebyshev polynomials in the solution of ordinary and partial differential equations
Chebyshev polynomials are used to obtain accurate numerical solutions of ordinary and partial differential equations. For functions of one or two variables, expressed in terms of ChebyshevExpand
An Overview of Software Development for Special Functions
This paper concentrates on the third step from the viewpoint of a numerical analyst working on software for elementary and special functions. Expand
A Survey of Practical Rational and Polynomial Approximation of Functions
This paper surveys current widely used methods for generating rational or polynomial approximations to continuous functions. Analytic methods and numerical algorithms are discussed with emphasis onExpand
Chebyshev expansions for the error and related functions
New 30 decimal place Chebyshev expansions, which can be used to obtain approximations up to that accuracy, for the error function and its complement are presented. Bilinear and biquadratic mappingsExpand
Diffraction and refraction calculations for waves incident on an island
An island of circular cylindrical shape, situated on a paraboloidal shoal (Fig. 1 and Table 1) in an infinite ocean of constant depth is attacked by small regular waves of long period and of planeExpand
Chebychev interpolations of the Gamma and Polygamma Functions and their analytical properties
Chebychev approximations are given for the Gamma and the Polygamma functions in only one contiguous intervall [1..inf] with a definable maximal relative error. The approximations need about threeExpand
Error Estimates for the
calculation of the error in terms of the function-values. In the present note we obtain error estimates for the Clenshaw-Curtis quadrature applied to functions analytic on the interval of integrationExpand
Finite element method with quasi-linearization for solving Bratu's problem
This work presented here is the solution of one-dimensional Bratu’s problem. The major aim of this research is to master the techniques used to solve the Bratu problem. The nonlinear Bratu’s Expand
Numerical Analysis for Engineers and Scientists
  • Gregory H. Miller
  • Mathematics
  • 2014
Preface 1. Numerical error 2. Direct solution of linear systems 3. Eigenvalues and eigenvectors 4. Iterative approaches for linear systems 5. Interpolation 6. Iterative methods and the roots ofExpand
Belief Propagation Decoding Algorithm via Tchebyshev-pad é Approximation for LDPC Codes ⋆
In this paper, a belief propagation (BP) decoding algorithm via Tchebyshev-Padé approximation is proposed for low-density parity-check (LDPC) codes. Compared with the standard BP decoding algorithm,Expand