TY - JOUR
T1 - On the choice of β in the u - transformation for convergence acceleration
AU - Abdalkhani, Javad
AU - Levin, David
N1 - Publisher Copyright:
© 2014, Springer Science+Business Media New York.
PY - 2015/9/28
Y1 - 2015/9/28
N2 - The influence of the shift parameter β upon the convergence of the u-transformation may be crucial. It is shown, through a specific example, that a clever choice of β can improve the convergence acceleration rate of the u-transformation, while a wrong choice may even imply divergence of the method. A constructive approach for choosing an optimal shift parameter β is presented, based upon the exactness class (model) of the u-transformation. The parameter β which defines the best fitted model to a specific sequence is chosen for the acceleration of that sequence.
AB - The influence of the shift parameter β upon the convergence of the u-transformation may be crucial. It is shown, through a specific example, that a clever choice of β can improve the convergence acceleration rate of the u-transformation, while a wrong choice may even imply divergence of the method. A constructive approach for choosing an optimal shift parameter β is presented, based upon the exactness class (model) of the u-transformation. The parameter β which defines the best fitted model to a specific sequence is chosen for the acceleration of that sequence.
KW - Convergence
KW - Nonlinear sequence transformations
KW - Parameter optimization
KW - u- transformation
UR - http://www.scopus.com/inward/record.url?scp=84940597922&partnerID=8YFLogxK
U2 - 10.1007/s11075-014-9942-9
DO - 10.1007/s11075-014-9942-9
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AN - SCOPUS:84940597922
SN - 1017-1398
VL - 70
SP - 205
EP - 213
JO - Numerical Algorithms
JF - Numerical Algorithms
IS - 1
ER -