Skip to Main Content

Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

An acceleration method for the power series of entire functions of order $1$
HTML articles powered by AMS MathViewer

by B. Gabutti and J. N. Lyness PDF
Math. Comp. 39 (1982), 587-597 Request permission

Abstract:

When $f(z)$ is given by a known power series expansion, it is possible to construct the power series expansion for $f(z;p) = {e^{ - pz}}f(z)$. We define ${p_{{\text {opt}}}}$ to be the value of p for which the expansion for $f(z;p)$ converges most rapidly. When $f(z)$ is an entire function of order 1, we show that ${p_{{\text {opt}}}}$ is uniquely defined and may be characterized in terms of the set of singularities ${z_i} = 1/{\sigma _i}$ of an associated function $h(z)$. Specifically, it is the center of the smallest circle in the complex plane which contains all points ${\sigma _i}$.
References
Similar Articles
  • Retrieve articles in Mathematics of Computation with MSC: 65B10, 30B10
  • Retrieve articles in all journals with MSC: 65B10, 30B10
Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Math. Comp. 39 (1982), 587-597
  • MSC: Primary 65B10; Secondary 30B10
  • DOI: https://doi.org/10.1090/S0025-5718-1982-0669651-0
  • MathSciNet review: 669651