Convergence Acceleration and Improvement by Regular Matrices

DOI10.1007/978-981-10-0913-6_4zbMath1357.40003OpenAlexW2475852652MaRDI QIDQ2826017

Ants Aasma

Publication date: 14 October 2016

Published in: Current Topics in Summability Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-981-10-0913-6_4

zbMATH Keywords

convergence accelerationregular matrix methodsorder of approximation of Fourier expansions

Mathematics Subject Classification ID

Matrix methods for summability (40C05) Extrapolation to the limit, deferred corrections (65B05) Approximation to limiting values (summation of series, etc.) (40A25) Research exposition (monographs, survey articles) pertaining to sequences, series, summability (40-02)

Uses Software

• hp.sr

Cites Work

• Padé-type rational and barycentric interpolation
• Richardson extrapolation on some recent numerical quadrature formulas for singular and hypersingular integrals and its study of stability
• A generalization of the \(G\)-transformation and the related algorithms
• Extensions of Drummond's process for convergence acceleration
• Survey of numerical stability issues in convergence acceleration
• Acceleration of convergence of general linear sequences by the Shanks transformation
• Similarities of the integral Padé approximants. II
• Programs for the approximation of real and imaginary single- and multi-valued functions by means of Hermite-Padé-approximants
• Convergence acceleration of series through a variational approach
• Further development of the new algorithms for accelerating the convergence of functional-type sequences
• A new method for accelerating convergence of alternating series
• Introduction to the determinantal formulae for the Levin-type algorithms
• A family of the functional epsilon algorithms for accelerating convergence
• Contraction properties of sequence transformations
• Nonexistence of universally accelerating linear summability methods
• Several remarks on acceleration of convergence using generalized linear methods of summability
• Introduction to the improved Levin-type algorithms for accelerating convergence of sequence.
• Extrapolation algorithms for filtering series of functions, and treating the Gibbs phenomenon
• New vector sequence transformations
• New representations of Padé, Padé-type, and partial Padé approximants
• Convergence analysis of the summation of the factorially divergent Euler series by Padé approximants and the delta transformation
• Generalizations of aitken's process for accelerating the convergence of sequences
• Development of the Overholt transformation for accelerating the convergence of sequences
• Development of the Levin-type algorithms for accelerating convergence of sequences
• Multistep $𝜖$–algorithm, Shanks’ transformation, and the Lotka–Volterra system by Hirota’s method
• Convergence Acceleration Algorithm via an Equation Related to the Lattice Boussinesq Equation
• Confluent Form of the Multistep ɛ-Algorithm, and the Relevant Integrable System
• STRONG Μ‐FASTER CONVERGENCE AND STRONG Μ‐ACCELERATION OF CONVERGENCE BY REGULAR MATRICES
• On the acceleration of convergence by regular matrix methods
• Asymptotic analysis of a generalized Richardson extrapolation process on linear sequences
• Convergence acceleration during the 20th century
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