Convergence Acceleration Of K-Periodic(k≥2) Continued Fractions

Convergence acceleration is important in the theory of continued fractions. Value may often be determined more quickly by using modifying factors. If continued fraction is limit k-periodic, a natural choice for the modifying factors is a k-periodic sequence. Clearly, the difficulty is to find suitable modifying factors when period k≥2.Firstly, we introduce some definitions and basic concepts about continued fractions. Secondly, we summarize the convergence acceleration about limit periodic continued fractions and limit k-periodic continued fractions.Thirdly, a new method to compute the converging factors for limit periodic continued fractions is given, by using of the property of limit 2—periodic continued fractions.A new approach to compute the limit 2-periodic continued fractions is given by means of the property of contractions. The choosing of modifying factors will become easy by use of the new algorithm.