TY - JOUR
T1 - Rational approximations from the d-transformation
AU - Sidi, Avram
AU - Levin, David
PY - 1982/4
Y1 - 1982/4
N2 - Recently the authors have presented the d-transformation which has proved to be very efficient in accelerating the convergence of a large class of infinite series. In this work the d-transformation is modified in a way that suits power series. An economical method for computing the rational approximations arising from the modified transformation is developed. Some properties of these approximants, similar to those of the Padé approximants, are derived. In the course of development a class of power series to which these rational approximations can be applied efficiently is characterized. A numerical example, showing the strong convergence properties of the approximations is appended and a comparison with the corresponding Padé approximants is given.
AB - Recently the authors have presented the d-transformation which has proved to be very efficient in accelerating the convergence of a large class of infinite series. In this work the d-transformation is modified in a way that suits power series. An economical method for computing the rational approximations arising from the modified transformation is developed. Some properties of these approximants, similar to those of the Padé approximants, are derived. In the course of development a class of power series to which these rational approximations can be applied efficiently is characterized. A numerical example, showing the strong convergence properties of the approximations is appended and a comparison with the corresponding Padé approximants is given.
UR - http://www.scopus.com/inward/record.url?scp=0040281096&partnerID=8YFLogxK
U2 - 10.1093/imanum/2.2.153
DO - 10.1093/imanum/2.2.153
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AN - SCOPUS:0040281096
SN - 0272-4979
VL - 2
SP - 153
EP - 167
JO - IMA Journal of Numerical Analysis
JF - IMA Journal of Numerical Analysis
IS - 2
ER -