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A Method of Accelerating Convergence for Infinite Sequence(PDF)

《南京理工大学学报》(自然科学版)[ISSN:1005-9830/CN:32-1397/N]

Issue:
1998年06期
Page:
573-576
Research Field:
Publishing date:

Info

Title:
A Method of Accelerating Convergence for Infinite Sequence
Author(s):
Shan Huaning
Mathematical and Physical Teaching Office,Naval Medical College,Nanjing2 10 0 99
Keywords:
inf inite sequences accelerat ion co nverg ence
PACS:
O241
DOI:
-
Abstract:
In this paper, w ith the method of accelerat ing conver gence of inf inite sequence, based on Levin t-t ransfo rm and it s iterat ive process , the iter at ion method of Lev in-t t ransfo rm is presented. It is pointed out that this metho d can increase the rate of co nverg ence of sequence, and it is confirmed by the specif ic ex amples. At the same t ime, this method fo rms a procedure of successive accelerat ion, and it is applicable fo r comput ing in computer . The method of fers obvious advantag es in pract ical use, especially in accelerat ing convergence of alterat ing series sequences.

References:

1  Lev in D. Develo pments o f non-linear tr ansfo rmat ions fo r impro ving conver gence o f sequences. Inter nat J Comput Math Ser B, 1973, 3( 3) : 371~388
2 Smit h D A, For d W F. Acceleration o f linear and log arithmic co nver gence. SIAM J Numer Anal, 1979, 16( 2) : 223~240
3 朱功勤, 顾传青. 一般外推算法的连续加速过程. 数值计算与计算机应用, 1992, 13( 1) : 13~19
4  Osada N. A conv erg ence acceler ation method for some lo gar ithmically conv erg ent sequence . SIAM J Numer Ana l, 1990, 27( 4) : 178~189
5 Drummo nd J E. Conver g ence speeding , conv erg ence and summabilit y, J Comput Appl Mat h,1984, 11( 3) : 145~ 159

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Last Update: 2013-03-29