A method of solving systems of nonlinear equations for use in metrological applications based on the generalized method of bisection is presented. It is shown that through the use of the proposed approach it is possible to satisfy requirements imposed on the solution as regards the set of results of indirect measurements and to take into account data on the inaccuracy of the coefficients of the equations to be solved, which are the results of direct measurements. The resulting solution is automatically tracked by a reliable estimate of the limiting error of its components.
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References
A. G. Chunovkina, V. A. Slaev, A. V. Stepanov, and N. D. Zvyagin, “Estimation of uncertainty of measurements with the use of data processing programs,” Izmer. Tekhn., No. 7, 3–8 (2008).
K. K. Semenov and A. A. Tselishcheva, “Integral method of bisection for metrologically based search for the roots of equations with inaccurately specified initial data,” Izmer. Tekhn., No. 3, 10–15 (2018).
D. Bachrathy and G. Stepan, “Bisection method in higher dimensions and the efficiency number,” Period. Polytechn. Mech. Eng., 56, No. 2, 81–86 (2012).
K. K. Semenov and G. N. Solopchenko, “Investigation of compound method of metrological self-tracking of programs for processing measurement results,” Izmer. Tekhn., No. 4, 14–19 (2011).
Yu. Z. Aleshkov, Theory of Waves on the Surface of a Heavy Fluid, Izd. Leningrad. Univ., Leningrad (1981).
V. A. Maksimov, I. S. Nudner, K. K. Semenov, and N. D. Titova, “Establishing the elevation of a wave surface from values of the hydrodynamic pressure throughout the depth of a fluid within the framework of the theory of surface waves (third approximation),” in: Proc. Int. Conf. Mathematical and Information Technologies, MIT-2013, Stamparija Ofsetpres, Kraljevo, Belgrade (2014), pp. 438–442.
M. V. Zhelamskii, “Features in the measurement of a local magnetic positioning field at short distances,” Izmer. Tekhn., No. 9, 39–43 (2014).
M. V. Zhelamskii, “Features in the creation of a positioning field for local navigation in closed spaces,” Izmer. Tekhn., No. 7, 40–44 (2014).
M. V. Zhelamskii, Electromagnetic Positioning of Moving Objects, Fizmatgiz, Moscow (2013).
M. V. Zhelamskii, K. K. Semenov, and G. N. Solopchenko, “Features in the calculation of the coordinates of a positioned object from the results of magnetic measurements,” in: Proc. Sci. Studies of 4th Int. Sci. Appl. Conf. Measurements in the Modern World – 2013, Izd. Politechn. Univ., St. Petersburg (2013), pp. 135–137.
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Translated from Izme ritel’naya Tekhnika, No. 3, pp. 13–18, March, 2019.
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Semenov, K.K., Tselishcheva, A.A. Generalized Interval Method of Bisection for Metrologically Based Search for Solutions of Systems of Equations with Inaccurately Specified Initial Data. Meas Tech 62, 193–201 (2019). https://doi.org/10.1007/s11018-019-01606-0
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DOI: https://doi.org/10.1007/s11018-019-01606-0