The simplified topological \(\varepsilon\)-algorithms: software and applications

DOI10.1007/s11075-016-0238-0zbMath1362.65004OpenAlexW2560488944MaRDI QIDQ521935

Claude Brezinski, Michela Redivo-Zaglia

Publication date: 12 April 2017

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

Full work available at URL: https://doi.org/10.1007/s11075-016-0238-0

zbMATH Keywords

softwaresystem of nonlinear equationsconvergence accelerationextrapolationnonlinear matrix equationmatrix functionssolution of equations

Mathematics Subject Classification ID

Related Items (11)

Geometrical inverse matrix approximation for least-squares problems and acceleration strategies ⋮ Shanks function transformations in a vector space ⋮ Shanks Sequence Transformations and Anderson Acceleration ⋮ The genesis and early developments of Aitken's process, Shanks' transformation, the \(\varepsilon\)-algorithm, and related fixed point methods ⋮ Matrix completion with \(\varepsilon\)-algorithm. In memory of Peter Wynn (1931--2017) ⋮ Image reconstruction and restoration using the simplified topological \(\varepsilon\)-algorithm ⋮ Extrapolation methods for the numerical solution of nonlinear Fredholm integral equations ⋮ A survey of Shanks' extrapolation methods and their applications ⋮ Matrix Shanks Transformations ⋮ Some unusual results on extrapolation methods ⋮ Extrapolation and prediction of sequences in a vector space

Uses Software

• Matlab
• TensorToolbox
• mctoolbox
• EPSfun
• mftoolbox

Cites Work

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• Extrapolation methods theory and practice
• Numerical stability of a quadratic method for solving systems of non linear equations
• Some results and applications about the vector \(\varepsilon\)-algorithm
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• On the numerical solution of a nonlinear matrix equation in Markov chains
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• Matrix polynomial and epsilon-type extrapolation methods with applications
• General purpose vector epsilon algorithm ALGOL procedures
• Convergence Rate of an Iterative Method for a Nonlinear Matrix Equation
• The Simplified Topological $\varepsilon$-Algorithms for Accelerating Sequences in a Vector Space
• Nonlinearly Preconditioned Inexact Newton Algorithms
• Functions of Matrices
• On the Solution of Systems of Equations by the Epsilon Algorithm of Wynn
• Singular rules for certain non-linear algorithms
• On a Device for Computing the e m (S n ) Transformation

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