Accelerating Convergence in Series and Infinite Integrals: Revisiting Levin and Sidi's Contributions
David Levin
TL;DR
This paper reviews the 1981 contributions of Levin and Sidi on nonlinear transformations that significantly improve the convergence of slowly converging series and infinite integrals, impacting numerical analysis.
Contribution
It revisits and evaluates the mathematical foundations, practical applications, and legacy of Levin and Sidi's nonlinear transformations for convergence acceleration.
Findings
The d-transformation effectively accelerates series convergence.
The D-transformation improves the evaluation of infinite integrals.
Their methods have a lasting impact on numerical analysis.
Abstract
The evaluation of slowly converging series and infinite integrals is a key challenge in numerical analysis and computational mathematics. In their influential 1981 paper, the author and Avram Sidi introduced two effective nonlinear transformations, the d-transformation for series and the D-transformation for infinite integrals, aimed at speeding up their convergence. This review summarizes, contextualizes, and evaluates their contributions, highlighting the mathematical basis, practical significance, and legacy of their work.
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Taxonomy
TopicsMathematical and Theoretical Analysis · Polynomial and algebraic computation · Iterative Methods for Nonlinear Equations