合成序列变换的加速收敛

CONVERGENCE ACCELERATION OF COMPOSITE SEQUENCE TRANSFORMATIONS

设{Sn}是待加速的序列,limSn=S。按[1]考虑序列变换tk:{Sn}→{tkn,k=1,2。记 Nk={{Sn}:?N,n>N,tkn=S},称Nk（k=1,2）是变换tk的核。定义变换T T:{Sn}→{Tn}, ?n,Tn=（1-αn）t1n+αnt2n,并规定,若Sn∈N1,则?n,αn=0,若Sn∈N2,则?n,αn=1。此时称T是秩为2的合成序列变换。 记N是变换T的核,则N?N1∪N2。由此说明变换T优于变换t1和变换t2。

Brezinski (1985) introduced the new concept of composite sequence transformation in [1].The aim of this paper is to study its convergence acceleration in the case of Aitken's Δ~2 process,Some results concerning the convergence of a comporite sequence are given; the limit of thesequence to be accelerated is not included in the conditions.