A methodology to transform dense to band matrices is presented in this paper. This transformation, is accomplished by triangular blocks partitioning, and allows the implementation of solutions to problems with any given size, by means of contraflow systolic arrays, originally proposed by H.T. Kung. Matrix-vector and matrix-matrix multiplications are the operations considered here.The proposed transformations allow the optimal utilization of processing elements (PEs) of the systolic array when dense matrix are operated. Every computation is made inside the array by using adequate feedback. The feedback delay time depends only on the systolic array size.

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