In this paper, we show that every systolic array executes a Regular Iterative Algorithm with a strongly separating hyperplane and conversely, that every such algorithm can be implemented on a systolic array. This characterization provides us with an unified framework for describing the contributions of other authors. It also exposes the relevance of many fundamental concepts that were introduced in the sixties by Hennie, Waite and Karp, Miller and Winograd, to the present day concern of systolic array