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Truncation error analysis by means of approximant systems and inclusion regions

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Summary

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, approximate integration, an iterative method for solving equations, Padé approximants and continued fractions.

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Authors and Affiliations

  1. University of Colorado, 80302, Boulder, Colorado, USA

    William B. Jones & W. J. Thron

Authors
  1. William B. Jones
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  2. W. J. Thron
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Additional information

Research supported in part by the National Science Foundation under Grant No. MPS 74-22111 and by the Air Force Office of Scientific Research, Air Force Systems Command, USAF, under Grant No. AFOSR-70-1888. The United States Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation hereon

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Jones, W.B., Thron, W.J. Truncation error analysis by means of approximant systems and inclusion regions. Numer. Math. 26, 117–154 (1976). https://doi.org/10.1007/BF01395969

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