Error Estimate for the Displacement Method

  • V. A. GoloveshkinEmail author
  • S. Yu. Solov’evEmail author


The problem of constructing an explicit formula for a majorant of a number sequence specified by recurrence relations is considered. Problems of this kind arise when estimating the error of recursive methods for calculating certain functions of a real variable. A special approach to studying the given recurrence relations is proposed in this work, based on which it is established that a majorant can be provided by a quite specific formula and belongs to the class of subexponential functions.


recurrence relation recursive algorithm function of a real variable method error subexponential function 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    S. Yu. Solov’ev, “An algorithm for calculating logarithms through displacement,” Mosc. Univ. Comput. Math. Cybern. 37, 83 (2013).CrossRefzbMATHGoogle Scholar
  2. 2.
    V. V. Bykova, “Mathematical methods for the analysis of recursive algorithms,” Zh. Sib. Univ., Ser. Mat. Fiz. 1(3), 236–246 (2008).Google Scholar
  3. 3.
    V. A. Ilyin and E. G. Poznyak, Fundamentals of Mathematical Analysis (Nauka, Moscow, 1998; Mir, Moscow, 1982), Part 1.Google Scholar
  4. 4.
    V. A. Goloveshkin and M. V. Ul’yanov, “Complexity classification method for algorithms based on angular measure of functions’ asymptotic increase,” Vychisl. Tekhnol. 11(1), 52–62 (2006).zbMATHGoogle Scholar

Copyright information

© Allerton Press, Inc. 2019

Authors and Affiliations

  1. 1.Institute of Applied MechanicsRussian Academy of SciencesMoscowRussia
  2. 2.MIREA—Russian Technological UniversityMoscowRussia
  3. 3.Department of Computational Mathematics and CyberneticsMoscow State UniversityMoscowRussia

Personalised recommendations