A challenging test for convergence accelerators: summation of a series with a special sign pattern.
A matrix analysis of the stability of the Clenshaw algorithm.
A symbolic operator approach to power series transformation-expansion formulas.
Accelerating the Convergence of a Table with Multiple Entry
Accelerating the Convergence of Power Series of Certain Entire Functions.
Algorithmes pour suites non convergentes.
Analytic Representations Suitable for Numerical Computation of Some Special Functions.
Approximants de Padé-Hermite. 1ère partie: théorie.
Approximants de Padé-Hermite. 2ème partie: programmation.
Brève communication. Transformations de suites
Composite Sequence Transformations.
Convergence acceleration of alternating series.
Convergence Acceleration of Some Sequences by the e-Algorithm.
Efficient representations of Green’s functions for some elliptic equations with piecewise-constant coefficients
Convenient for immediate computer implementation equivalents of Green’s functions are obtained for boundary-contact value problems posed for two-dimensional Laplace and Klein-Gordon equations on some regions filled in with piecewise homogeneous isotropic conductive materials. Dirichlet, Neumann and Robin conditions are allowed on the outer boundary of a simply-connected region, while conditions of ideal contact are assumed on interface lines. The objective in this study is to widen the range of...
Efficient Stable Ways to Calculate Continued Fraction Coefficients From some Series.
Evaluation of coefficients of a double Chebyshev series of the function g(p(x+y))
Fast multilevel evaluation of smooth radial basis function expansions.
Forme confluente de l'e-algorithme topologique.
Formulas for sums of powers of integers by functional equations.
Nilakantha's accelerated series for π
We show how the idea behind a formula for π discovered by the Indian mathematician and astronomer Nilakantha (1445-1545) can be developed into a general series acceleration technique which, when applied to the Gregory-Leibniz series, gives the formula with convergence as , in much the same way as the Euler transformation gives with convergence as . Similar transformations lead to other accelerated series for π, including three “BBP-like” formulas, all of which are collected in the Appendix....