Algebraic properties of the E-transformation
Claude Brezinski (1990)
Banach Center Publications
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Displaying similar documents to “A challenging test for convergence accelerators: summation of a series with a special sign pattern.”
Algebraic properties of the E-transformation
Some results on convergence acceleration for the E-algorithm
A. Fdil (1997)
Applicationes Mathematicae
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Some new results on convergence acceleration for the E-algorithm which is a general extrapolation method are obtained. A technique for avoiding numerical instability is proposed. Some applications are given. Theoretical results are illustrated by numerical experiments
Convergence acceleration by the -algorithm
A. Fdil (1998)
Applicationes Mathematicae
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A new algorithm which generalizes the E-algorithm is presented. It is called the -algorithm. Some results on convergence acceleration for the -algorithm are proved. Some applications are given.
Bordering methods and progressive forms for sequence transformations
C. Brezinski (1988)
Applicationes Mathematicae
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On the convergence of SCF algorithms for the Hartree-Fock equations
Eric Cancès, Claude Le Bris (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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The present work is a mathematical analysis of two algorithms, namely the Roothaan and the level-shifting algorithms, commonly used in practice to solve the Hartree-Fock equations. The level-shifting algorithm is proved to be well-posed and to converge provided the shift parameter is large enough. On the contrary, cases when the Roothaan algorithm is not well defined or fails in converging are exhibited. These mathematical results are confronted to numerical experiments performed by...