A note on the summation of Chebyshev series

  title={A note on the summation of Chebyshev series},
  author={C. W. Clenshaw},
  journal={Mathematics of Computation},
Solving the linear semiclassical Schrödinger equation on the real line
The main idea is to derive the solution using a spectral method from a combination of solutions of the free Schrödinger equation and of linear scalar ordinary differential equations, in a symmetric Zassenhaus splitting method. Expand
Signal flow graph approach to inversion of (H,m)-quasiseparable-Vandermonde matrices and new filter structures
Abstract We use the language of signal flow graph representation of digital filter structures to solve three purely mathematical problems, including fast inversion of certain polynomial-VandermondeExpand
A unified approach to the Clenshaw summation and the recursive computation of very high degree and order normalised associated Legendre functions
Abstract. Spherical harmonic expansions form partial sums of fully normalised associated Legendre functions (ALFs). However, when evaluated increasingly close to the poles, the ultra-high degree andExpand
An Analogue for Szeg } o Polynomials of the Clenshaw AlgorithmGregory
Linear combinations of polynomials that are orthogonal with respect to an inner product deened on (part of) the real axis are commonly evaluated by the Clenshaw algorithm. We present an analogousExpand
Recurrence relations for the Cartesian derivatives of the Zernike polynomials.
  • Philip Stephenson
  • Mathematics, Medicine
  • Journal of the Optical Society of America. A, Optics, image science, and vision
  • 2014
A recurrence relation for the first-order Cartesian derivatives of the Zernike polynomials is derived. This relation is used with the Clenshaw method to determine an efficient method for calculatingExpand
On Satellite Gravity Gradiometry
Non-singular expressions for the vector and the gradient tensor of gravitation in a geocentric spherical frame
  • M. Eshagh
  • Computer Science, Mathematics
  • Comput. Geosci.
  • 2008
Alternative expressions for the GV and GGT are presented, which are independent of the derivatives, and are also non-singular, and suffices to compute the ALF to two additional degrees and orders, instead of computing the first and the second derivatives of all the ALf. Expand
A summation technique for minimal solutions of linear homogeneous difference equations
A computationally economic summation technique for minimal solutions of linear homogeneous difference equations of arbitrary order is presented. Its numerical stability is shown by means of aExpand
Product integration with the Clenshaw-Curtis points: Implementation and error estimates
SummaryThis paper is concerned with the practical implementation of a product-integration rule for approximating $$\int\limits_{ - 1}^1 {k(x)f(x)dx} $$ , wherek is integrable andf is continuous. TheExpand


Polynomial approximations to elementary functions
Graphs of and pass through The approximating polynomial is said to be expanded about c or centered at c. Geometrically, the requirement that means that the graph of passes through the point OfExpand