The genesis and early developments of Aitken's process, Shanks' transformation, the \(\varepsilon\)-algorithm, and related fixed point methods

DOI10.1007/s11075-018-0567-2zbMath1477.65011OpenAlexW2888051195MaRDI QIDQ1710714

Michela Redivo-Zaglia, Claude Brezinski

Publication date: 23 January 2019

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-018-0567-2

zbMATH Keywords

fixed pointsextrapolationAnderson accelerationMPEAitken's processepsilon-algorithmsMMPEPulay mixingRREShanks' transformations

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Extrapolation to the limit, deferred corrections (65B05) Iterative numerical methods for linear systems (65F10) History of numerical analysis (65-03) Numerical methods for difference equations (65Q10)

Related Items

Geometrical inverse matrix approximation for least-squares problems and acceleration strategies, Convergence of a Constrained Vector Extrapolation Scheme, Generalizations of Shanks transformation and corresponding convergence acceleration algorithms via Pfaffians, On the kernel of vector \(\varepsilon \)-algorithm and related topics, Generalized discrete Lotka-Volterra equation, orthogonal polynomials and generalized epsilon algorithm, Acceleration of sequences with transformations involving hypergeometric functions, An application of a qd‐type discrete hungry Lotka–Volterra equation over finite fields to a decoding problem, Reuben Louis Rosenberg (1909--1986) and the Stein-Rosenberg theorem, Matrix completion with \(\varepsilon\)-algorithm. In memory of Peter Wynn (1931--2017), Functions and eigenvectors of partially known matrices with applications to network analysis, A survey of Shanks' extrapolation methods and their applications, Construction of new generalizations of Wynn's epsilon and rho algorithm by solving finite difference equations in the transformation order, A novel iterative method for discrete Helmholtz decomposition, Some unusual results on extrapolation methods, On the Effectiveness of Richardson Extrapolation in Data Science, Extrapolation and prediction of sequences in a vector space

Uses Software

• Maple
• Matlab
• SQUAREM
• Anderson
• EPSfun
• ALGOL 60
• GRPIA

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