This article is cited in 1 paper

NUMERICAL METHODS AND ALGORITMS

On the convergence of some algorithms of binary or ternary machine arithmetic for calculations in imaginary quadratic fields

P. S. Bogdanov<sup>ab

a</sup> Samara State Aerospace University
^b Image Processing Systems Institute, Russian Academy of Sciences

Abstract: The paper proves a number of statements that significantly reduce the complexity of proofs of the classification theorems for quasicanonical number systems in imaginary quadratic fields. Theorems on convergence of algorithms that implement the addition of algebraic integers in quasicanonical number systems are proved.

Keywords: canonical numerical system, quasicanonical numerical system, norm division with remainder, equivalent numerical systems.

Received: 24.02.2015
Revised: 08.04.2015

DOI: 10.18287/0134-2452-2015-39-2-249-254