Parallelization of recurrent loops due to the preliminary computation of superpositions

As a rule, sections of code that take a lot of time to compute are loops. Therefore, it is precisely on them that special efforts are directed when accelerating programs, in particular, through parallelization.
The article describes the parallelization algorithm for loops calculating the elements of a recursively given sequence. The recurrent loops considered in the article cannot be directly parallelized. With the help of auxiliary transformations, they can sometimes be reduced to loops that allow parallel execution. Earlier, the author of the article published another algorithm for parallelizing loops that calculate the elements of a recursively given sequence.
In modern processors, the execution time of arithmetic operations is an order of magnitude faster than reading the arguments of these operations from RAM. This article provides estimates of the complexity of accessing memory for the described algorithm. The parallel algorithm presented in the article is more efficient in accessing memory than the algorithm described by the author earlier.