A lag-average generalization of Euler's method for accelerating series

DOI10.1016/0096-3003(94)00180-CzbMath0838.65002MaRDI QIDQ1907080

John P. Boyd

Publication date: 3 June 1996

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

zbMATH Keywords

comparison of methodsconvergence accelerationRichardson extrapolationsummation of seriesepsilon algorithmEuler acceleration methodlag-averaging

Mathematics Subject Classification ID

Extrapolation to the limit, deferred corrections (65B05) Numerical summation of series (65B10)

Related Items

Numerical inversion for Laplace transforms of functions with discontinuities ⋮ A Proof, Based on the Euler Sum Acceleration, of the Recovery of an Exponential (Geometric) Rate of Convergence for the Fourier Series of a Function with Gibbs Phenomenon ⋮ A proof that the discrete singular convolution (DSC)/Lagrange-distributed approximating function (LDAF) method is inferior to high order finite differences ⋮ Construction of Lanczos type filters for the Fourier series approximation ⋮ Acceleration of algebraically-converging Fourier series when the coefficients have series in powers of \(1/n\) ⋮ Trigonometric approximation of periodic functions belonging to \(\mathrm{Lip}(\omega(t), p)\)-class ⋮ Optimal filter and mollifier for piecewise smooth spectral data ⋮ An asymptotically hierarchy-consistent, iterative sequence transformation for convergence acceleration of Fourier series ⋮ Compatibility conditions for time-dependent partial differential equations and the rate of convergence of Chebyshev and Fourier spectral methods ⋮ Computation of irregularly oscillating integrals ⋮ On the Convergence of the Quasi-Periodic Approximations on a Finite Interval

Uses Software

• Algorithm 38

Cites Work

• Unnamed Item
• Sum-accelerated pseudospectral methods: The Euler-accelerated sinc algorithm
• Sequence transformations and their applications
• Algorithm 38. Two computer codes for convergence acceleration
• Convergence acceleration on a general class of power series
• Numerical Comparisons of Nonlinear Convergence Accelerators
• Acceleration of Linear and Logarithmic Convergence
• Convergence acceleration from the point of view of linear programming
• A note on the generalised Euler transformation
• Singular rules for certain non-linear algorithms
• Rational Chebyshev spectral methods for unbounded solutions on an infinite interval using polynomial-growth special basis functions

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