Semenchuk A. Recurrence fractions and their convergence.

Thesis is devoted to the investigation of recurrence fractions of 3-order, as one of the generalizations of continued fractions. In particular, established connection of recurrence periodical fractions of 3-order with real positive roots of some cubic equation. Built an algorithm for computing rational estimations of recurrence periodical fraction of 3-order. Also, established connection of mixed of recurrence periodical fractions of 3-order, net of recurrence periodical fractions of 3-order with real positive roots corresponding cubic equations. Built an algorithm for computing rational estimations of mixed of recurrence periodical fraction of 3-order. Investigated of convergence of recurrence 1-periodical fractions of 3-order and set the appropriate evaluation of error rational estimations shortened to values recurrence fractions.Besides, an investigated of cubic form and form of 4-degree. In particular, built some algorithms for computing cubic fields and fields of 4-degree.