Transformation of the systolic arrays from two-dimensional to linear form

The basic problems of linear algebra, such as the solution of linear systems, triangular decomposition and matrix multiplication, are computationally expansive. So, there is a need to solve those problems with systolic structures, where many processors are used concurrently to compute the result. But, since a two-dimensional array of processors is very space- and resource-consumptive, it is better to use a one-dimensional array of processors. However, this leads to the problem of operation reallocation and unequal utilization of processors, but it is easier to implement since there is only one straight array of processors. This paper presents the aforementioned transformations and their comparison.