Convergence acceleration for continued fractions

Author:
Lisa Jacobsen

Journal:
Trans. Amer. Math. Soc. **275** (1983), 265-285

MSC:
Primary 40A15; Secondary 30B70

DOI:
https://doi.org/10.1090/S0002-9947-1983-0678349-1

MathSciNet review:
678349

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Abstract | References | Similar Articles | Additional Information

Abstract: A known method for convergence acceleration of limit periodic continued fractions , is to replace the approximants by "modified approximants" , where . The present paper extends this idea to a larger class of converging continued fractions. The "modified approximants" will then be , where is a converging continued fraction whose tails are all known, and where .

As a measure for the improvement obtained by this method, upper bounds for the ratio of the two truncation errors are found.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1983-0678349-1

Keywords:
Continued fractions,
convergence acceleration,
uniform convergence regions

Article copyright:
© Copyright 1983
American Mathematical Society