FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2010, VOLUME 16, NUMBER 6, PAGES 95-108

Methods for estimating of continuants

I. D. Kan

Abstract

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The paper is concerned with special sets of continuants occuring in applications. For each of these sets, the problem of finding the maximal and minimal continuants is solved. Methods of finding these extrema are singled out and grouped. This results in the methods of basic permutations, quadratic irrationalities, unit variation, and majorizing inequalities. The lasted named one is the only method involving new ideas, the remaining ones were already examined in parts.

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Last modified: July 5, 2011