formulas of central finite differences

One of the main tasks of deploying sensor networks is determining the coordinates of nodes that are unknown at their initial placement. This problem is known as the localization problem of sensor networks. It can be solved if each node has a GPS receiver in its composition. However, such nodes are more expensive, and for networks of various purposes, for example, environmental monitoring, fixation of moving objects in a certain area, various types of IoT, and others, nodes without GPS can be used.

Noise generators and pseudorandom number generators (PRNGs) are widely used in the field of information technology, including cybersecurity, for modeling, authorization key generation, and technical protection of information. It has been found that the characteristics of digital noise directly depend on the chosen PRNG algorithm. To determine the quality of the generated noise, special tests are performed, which are primarily applied to the sequence generated by the PRNG.

A methodology has been developed for numerically differentiating table-given functions using a Taylor polynomial of degree n, which enables the computation of k-th order derivatives (k £ n) at any point between arbitrarily located interpolation nodes in one, two, or multiple independent variables. Recent research and publications have been analysed, allowing for the assessment of the task complexity of computing derivatives of a function based on the values of independent variables within a certain interval of a table-given function.