An approach to implicit structures of data constrained in computational procedures is presented herein. Transformations of them are looked for in order to obtain a desired effect of convergence in performed evaluations. First, a kinship between such structures has been elucidated by means of a resemblance comparator on weak Brouwerian lattices. Certain group representations introduced turned out to support suitable transformations imposed on the given set of data. An algorithm has been elaborated on the grounds of theoretical derivations. Data given by sets of multidimensional vectors were structured by associating elements of a Boolean ring (multidimensional bounded intervals) which enabled structural modifications. This yielded decreases of the function computed in an example of energy determination for the helium atom. The stabilization of data relationships was exercised in the course of computations. Skipping effect surpassing results of standard procedures circa 2500% has been shown and illustrated by relevant plots. The method is intended to open a way for a better efficiency in large scale computations, e.g., in many electron system evaluations with high accuracy. This should additionally be stressed that other approaches like extrapolations, genetic algorithrns, etc. have not equally approved their power in resolving hard problems of efficient convergence predictions.
Operational Program Digital Poland, 2014-2020, Measure 2.3: Digital accessibility and usefulness of public sector information; funds from the European Regional Development Fund and national co-financing from the state budget.
Oct 15, 2021
Aug 18, 2021