In the preprint «Continued fractions by the nearest even number», we propose a new type of one-dimensional continued fractions. It has many properties of the classic continued fractions: convergence, uniqueness of expansion, periodicity for quadratic irrationalities. But they converge very slow. Here we propose a fast (short) type of even continued fractions. The modi»ed algorithm allows to replace a sequence of similar parts of even continued fraction by one linear fractional transformation.

Mathematical problems and theory of numerical methods