Metrological Approach to Solve Nonlinear Equations and Systems of Nonlinear Equations
A. A. Tselishcheva, Konstantin K. Semenov · 2021
This paper presents an approach to solving nonlinear equations and systems of nonlinear equations that appear when performing indirect measurements, which fully satisfies the metrological requirements for their results. The proposed method is based on the bisection technique and allows obtain reliable estimates of the desired equations solutions and their uncertainty. At each iteration, the result is given as an interval, which is guaranteed to contain all possible values of the root or the system's solution as required from the measurement result. Therefore, if the iterative process is stopped too early for some reason, the measurement result will still be obtained, but the interval bounds will be wider than they should have been.