The Richardson Extrapolation Process with a Harmonic Sequence of Collocation Points

DOI10.1137/S0036142998340137zbMath0957.65002MaRDI QIDQ4509653

Avram Sidi

Publication date: 19 October 2000

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

zbMATH Keywords

stabilityconvergenceasymptotic expansionnumerical examplesnumerical quadratureRichardson extrapolationharmonic sequence of collocation points

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Extrapolation to the limit, deferred corrections (65B05) Numerical quadrature and cubature formulas (65D32) Approximation to limiting values (summation of series, etc.) (40A25) Numerical summation of series (65B10)

Related Items (8)

A convergence and stability study of the iterated Lubkin transformation and the $\theta$-algorithm ⋮ Extrapolation for solving a system of weakly singular nonlinear Volterra integral equations of the second kind ⋮ Survey of numerical stability issues in convergence acceleration ⋮ An extended multistep Shanks transformation and convergence acceleration algorithm with their convergence and stability analysis ⋮ Acceleration of convergence of general linear sequences by the Shanks transformation ⋮ A de Montessus type convergence study for a vector-valued rational interpolation procedure ⋮ A de Montessus type convergence study of a least-squares vector-valued rational interpolation procedure ⋮ New convergence results on the generalized Richardson extrapolation process GREP$^{(1)}$ for logarithmic sequences

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