ПРЕОБРАЗОВАНИЕ ПОСЛЕДОВАТЕЛЬНОГО ИНФОРМАЦИОННОГО ГРАФА МЕТОДА ПРОГОНКИ В ПАРАЛЛЕЛЬНУЮ ФОРМУ

Abstract

Many computational tasks can be represented in the form of a sequential information graph.In the general case, such an information graph cannot be reduced to a parallel form in order tospeed up the execution of its operations. But if the vertices of this graph have the properties ofassociativity, distributivity, etc., such a graph can be transformed into a parallel-pipeline form.These transformations can be performed not only on graphs containing elementary operations -addition, multiplication, logical AND, etc. - but also over graphs containing macro operations.One example of such graphs is the information graph for solving SLAEs by the sweep method(Thomas's method). The article considers a solution for tridiagonal linear systems. The informationgraph of the sweep method consists of two parts: the forward move, in which the transitionfrom the three-diagonal form to the two-diagonal form is performed, and the reverse move, inwhich the values of the variables are directly calculated. Despite the fact that the operations thatmake up the basic macro-operation of the sweep method have the property of associativity, a simpletransformation of the graph to a pyramidal form will not give the desired result. It is necessaryto transform the basic macro operations in a special way and change what data is received onthem. After that, it will be possible to bring the graph to a pyramidal form. For the reverse move, asimilar transformation of the graph and its constituent base subgraphs is applied. Since in order tostart computations in the reverse run, we need to complete the computations of the forward run,we should switch from two specialized types of computational blocks to one universal one, andbuild a universal computational structure on its basis.