- 1 - 1 . a Generalized Richardson Extrapolation
نویسنده
چکیده
A convergence result for a 'generalized Richardson extrapolation process is improved .upon considerably and additional results of interest are'proved. An application of practical importance is also given. T ec hn io n C om pu te r Sc ie nc e D ep ar tm en t T eh ni ca l R ep or t C S0 53 0 19 88
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Convergence Analysis for a Generalized Richardson Extrapolation Process with an Application to the ¿(^-transformation on Convergent and Divergent Logarithmic Sequences
In an earlier work by the author the Generalized Richardson Extrapolation Process (GREP) was introduced and some of its convergence and stability properties were discussed. In a more recent work by the author a special case of GREP, which we now call GREP(I) , was considered and its properties were reviewed with emphasis on oscillatory sequences. In the first part of the present work we give a ...
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The stability of a large class of nonlinear sequence transformations is analyzed. of the convergence behavior of the J transformation. Similar to recent results of Sidi, it is proved that the pJ transformations , the Weniger S transformation, the Levin transformation and a special case of the Generalized Richardson Extrapolation Process of Sidi are S-stable. An eecient algorithm for the calcula...
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Let a(t) ∼ A+ ’(t)∑∞i=0 it as t → 0+, where a(t) and ’(t) are known for 0¡t6c for some c¿ 0, but A and the i are not known. The generalized Richardson extrapolation process GREP is used in obtaining good approximations to A, the limit or antilimit of a(t) as t → 0+. The convergence and stability properties of GREP for the case in which ’(t) ∼ t as t → 0+; 6= 0;−1;−2; : : : ; have been studied t...
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In this work, we give a detailed convergence and stability analysis for the author’s generalized Richardson extrapolation process GREP(m) as this is being applied to linearly convergent or divergent infinite sequences {An}, where An ∼ A + ∑m k=1 ζ n k ∑∞ i=0 βkin γk−i as n → ∞, ζk = 1 being distinct. The quantity we would like to compute is A, whether it is the limit or antilimit of {An}. Such ...
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A convergence result for a generalized Richardson extrapolation process is improved upon considerably and additional results of interest are proved. An application of practical importance is also given. Finally, some known results concerning the convergence of Levin's T-transformation are reconsidered in light of the results of the present work. Let A(y) be a scalar function of a discrete or co...
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