Performance of arithmetical operations on mobile gadgets using axioms of classical and nonstandard interval analysis

Abstract

We propose a programming system for calculation of economical standards of regulating banking activity by means of Euclidian and interval arithmetic using mobile gadgets. The program was created by means of Microsoft Visual Studio 2017 Express for Windows Phone using C#.  The feature of this programming system is the possibility to be used anywhere: during business negotiations, in the absence of PCs and WiFi, etc. For its application, one needs a smartphone with Android operation system. The smartphone needs to have a capacitive screen with multi-touch input with the possibility of more than four touches at once. The size of the screen can vary, but the resolution must be 480*480 pixels. During the progress, the system calculates the indicators of banking activity approved by National bank of Ukraine. Using of the interval arithmetic gives the possibility to analyse the financial status of the bank under any conditions. The comparison of the results of arithmetical operations by using the axioms of classical and nonstandard interval analysis was carried out. The criterion of the efficiency is the value of the relative change of the final interval of the calculations that were carried out using the axioms of the nonstandard interval analysis related to the same calculations that were carried out using the axioms of the classical interval analysis. For efficiency comparison we choose standard indicators that define the financial safety of the bank. The results of the calculations show that the intervals defined according to the rules of the nonstandard interval mathematics have the size of the interval 12-90% less than the intervals calculated according to the rules of the classical interval mathematics.