D-calculus of One-dimensional Discrete Functions on a Non-uniform Grid

In this work the general method of construction of D-calculus of one-dimensional discrete functions on a non-uniform grid is developed. Initial prerequisites of construction are given. By changing corresponding initial prerequisites various realizations of D-calculus for some special cases of universal difference operator with lagging argument are constructed. D-calculus realizations are studied in detail and illustrated by examples. Interesting communications between trigonometrical functions and symmetric relation matrixes are found out. In such way has been found out a n-dimensional golden section which is the matrix description of regular 2(2n + 1)-gons.