Skip to main content
SpringerLink
Log in

Interval Method of Bisection for a Metrologically Based Search for the Roots of Equations with Inaccurately Specified Initial Data

  • GENERAL PROBLEMS OF METROLOGY AND MEASUREMENT TECHNIQUE
  • Published:
Measurement Techniques Aims and scope

A modification of the method of bisection for the purpose of searching for the root of a nonlinear equation is presented. Through the use of the modification, it becomes possible to use the method of bisection to solve equations of indirect measurements in full agreement with the metrological requirements imposed on the results of indirect measurements. It is shown that through the use of data on inaccuracies in the coefficients of equations that are the results of direct measurements it becomes possible to speed up the search for the root as well as achieving a reliable estimate of the characteristics of the error.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.

Similar content being viewed by others

References

  1. Yu. I. Shokin, Interval Analysis, Nauka, Novosibirsk (1981).

    MATH  Google Scholar 

  2. K. K. Semenov and G. N. Solopchenko, “A study of the combined method of metrological self-tracking of programs for processing the results of measurements,” Izmer. Tekhn., No. 4, 14–19 (2011).

    Google Scholar 

  3. V. Ya. Kreinovich and M. I. Pavlovich, “Estimation of the error of the result of indirect measurements by a computational experiment,” Izmer. Tekhn., No. 3, 11–13 (1985).

  4. V. A. Slaev and A. G. Chunovkina, Certification of Assurance Programs Used in Metrology: Handbook, Professional,St. Petersburg (2009).

    Google Scholar 

  5. G. N. Solopchenko, “Principles of normalization, determination, and control of the characteristics of error in computations performed in an information and measurement system,” Izmer. Tekhn., No. 3, 9–11 (1985).

  6. Yu. A. Kuderov, Yu. E. Lukashov, and A. A. Satanovskii, “Metrological certification of software of measuring instruments (state and outlook),” Zakonodat. Prikl. Metrol., No. 4, 39–44 (2003).

  7. L. I. Turchak, Foundations of Numerical Methods, Nauka, Moscow (1987).

    MATH  Google Scholar 

  8. A. Griewank, “On automatic differentiation,” in: Mathematical Programming: Recent Developments and Applications, M. Iri and K. Tanabe (eds.), Kluwer Academic (1989), pp. 83–108.

  9. GOST 6651–2009, Platinum, Nickel, and Copper and Nickel Thermal Converters.

  10. MEK 60751:2008, Industrial Platinum Resistance Thermometers and Platinum Temperature Sensors.

Download references

Author information

Authors and Affiliations

  1. Peter the Great St. Petersburg Polytechnic University, St. Petersburg, Russia

    K. K. Semenov & A. A. Tselishcheva

Authors
  1. K. K. Semenov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. A. Tselishcheva
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to K. K. Semenov.

Additional information

Translated from Izmeritel’naya Tekhnika, No. 3 pp. 10–15, March, 2018.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Semenov, K.K., Tselishcheva, A.A. Interval Method of Bisection for a Metrologically Based Search for the Roots of Equations with Inaccurately Specified Initial Data. Meas Tech 61, 203–209 (2018). https://doi.org/10.1007/s11018-018-1410-9

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11018-018-1410-9

Keywords

Search

Navigation