Truncation Error Analysis by Means of Approximant Systems and Inclusion Regions.

摘要

A general approach to truncation error analysis is described, in which bounds for the truncation error are determined by means of inclusion regions, and the notion of bestness is meaningfully formulated. A new mathematical structure (approximant system) is introduced and developed. It consists of a family of infinite processes having a natural structure for truncation error analysis. Applications of the methods are included for infinite series, Cesaro sums, approximant integration, an iterative method for solving equations, Pade approximants and continued fractions. (Author)