TY - JOUR
T1 - Accelerating infinite products
AU - Cohen, Alan M.
AU - Levin, David
PY - 1999
Y1 - 1999
N2 - Slowly convergent infinite products Π∞n=1 bn are considered, where {bn} is a sequence of numbers, or a sequence of linear operators. Using an asymptotic expansion for the "remainder" of the infinite product a method for convergence acceleration is suggested. The method is in the spirit of the d-transformation for series. It is very simple and efficient for some classes of sequences {bn}. For complicated sequences {bn} it involves the solution of some linear systems, but it is still effective.
AB - Slowly convergent infinite products Π∞n=1 bn are considered, where {bn} is a sequence of numbers, or a sequence of linear operators. Using an asymptotic expansion for the "remainder" of the infinite product a method for convergence acceleration is suggested. The method is in the spirit of the d-transformation for series. It is very simple and efficient for some classes of sequences {bn}. For complicated sequences {bn} it involves the solution of some linear systems, but it is still effective.
KW - Convergence acceleration
KW - Infinite products
UR - http://www.scopus.com/inward/record.url?scp=0033268348&partnerID=8YFLogxK
U2 - 10.1023/A:1019106823947
DO - 10.1023/A:1019106823947
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AN - SCOPUS:0033268348
SN - 1017-1398
VL - 22
SP - 157
EP - 165
JO - Numerical Algorithms
JF - Numerical Algorithms
IS - 2
ER -