On Shallit’s Minimization Problem

نویسندگان

چکیده

In Shallit’s problem (SIAM Review, 1994), it was proposed to justify a two-term asymptotics of the minimum rational function $$n$$ variables defined as sum special form whose number terms is order $$n^2$$ $$n\to\infty$$ . Of particular interest second term this (“Shallit’s constant”). The solution published in SIAM Review presented an iteration algorithm for calculating constant, which contained some auxiliary sequences with certain properties monotonicity. However, rigorous justification properties, necessary assert convergence process, replaced by reference numerical data. present paper, gaps proof are filled on basis analysis trajectories two-dimensional dynamical system discrete time corresponding points -sums. addition, sharp exponential estimate remainder asymptotic formula obtained.

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ژورنال

عنوان ژورنال: Mathematical Notes

سال: 2021

ISSN: ['1573-8876', '0001-4346', '1067-9073']

DOI: https://doi.org/10.1134/s0001434621090078