On Numerical Methods in Localization Problems

When solving localization problems numerically, the main task is to construct a universalsection corresponding to a given localizing function. The paper proposes two methods for solvingthis problem that use estimates of the first- and second-order derivatives. A comparative analysisof these methods with the method based on the use of all nodes of a regular grid is carried out. Acomparative analysis shows that the proposed methods are superior both in terms ofcomputational complexity and in the quality of the resulting approximation of the universalsection.