A truncation error bound for some branched continued fractions of the special form |
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| Author |
i.bilanyk@ukr.net
Pidstryhach Institute for Applied Problems of Mechanics and Mathematics
of the National Academy of Sciences of Ukraine, Lviv, Ukraine
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| Abstract |
By the analogy with continued fractions, the angular domain of convergence of branched
continued fraction of the special form is established. The truncation error bound for branched
continued fractions of the special form is established. For this we have used the estimates for
continued fractions obtained by J. Jensen, W. Gragg, D.Warner, the multidimensional analogue
of the van Vleck Theorem, the analytic theory of continued fractions and branched continued
fractions and the elements of the theory of stability under perturbations. In comparison with
already known results, in the paper, the conditions of isolation from zero for elements of
branched continued fractions of the special form are weakened, but there are some requirements
for the elements’ speed of tending to zero. The obtained result is a multidimensional analogue
of estimates for van Vleck continued fractions.
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| Keywords |
continued fraction; branched continued fraction of the special form; truncation error bound
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| DOI |
doi:10.30970/ms.52.2.115-123
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| Reference |
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| Pages |
115-123
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| Volume |
52
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| Issue |
2
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| Year |
2019
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| Journal |
Matematychni Studii
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| Full text of paper | |
| Table of content of issue |