We consider some number-theoretic modifications of algorithms transforming rational sequences. These algorithms are widely applicable in numerical analysis. We use them for construction of the regular continued fractions for some fundamental constants. These algorithms together with the Brun’s criterion allow in a number of cases to establish irrationality of the values algorithmically with the use of only the rational arithmetic.
Keywords:
Brun's criterion, regular continued fractions, irrationality proofs
Publication language:russian, pages:22
Research direction:
Mathematical problems and theory of numerical methods
