Abstract
A priori estimates are obtained for the truncation error of continued fractions of the formK(1/b n ), with complex elementsb n . The method employed is based on the calculation of bounds for successive diameters of a sequence of nested disks, where then-th approximant of the continued fraction is contained in then-th disk. Numerical examples are given to illustrate useful procedures and typical error estimates for continued fraction expansions of the complex logarithm and the ratio of consecutive Bessel functions.
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This research was supported by the National Science Foundation under Grant No. GP-9009 and by the United States Air Force through the Air Force Office of Scientific Research under Grant No. AFOSR-70-1888.
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Field, D.A., Jones, W.B. A priori estimates for truncation error of continued fractionsK(1/b n ) . Numer. Math. 19, 283–302 (1972). https://doi.org/10.1007/BF01404877
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DOI: https://doi.org/10.1007/BF01404877