Some characteristics of systolic arrays

We investigate a possible optimization of some linear algebra problems which can be solved by parallel processing using the special arrays called systolic arrays. In this paper are used some special types of transformations for the designing of this arrays. We show the characteristics of each one giving the examples of their implementation as well. The main focus is on discussing the advantages of these arrays in parallel computation of matrix product, with special approach to the designing of systolic array for matrix multiplication and discrete Fourier transformation. Multiplication of large matrices requires a lot of computational time and its complexity is O(n 3 ). There are developed many algorithms (both sequential and parallel) with the purpose of minimizing the time of calculations. Systolic arrays are good suited for these purpose. In this paper we show that using a appropriate composite function, the given index space can be mapped in another index space suitable for systolic array. This mapping implicates in finding more optimal arrays for doing the calculations of this type. We show that this can be implemented on the designing of optimal systolic array for Discrete Fourier transformation.