<p><it>Abstract—</it>A two-step regularization method in which first permutation sequences and then broadcast planes are selected is proposed to design various regular iterative algorithms for matrix multiplication. The regular iterative algorithms are then spacetime mapped to regular arrays, such as mesh, cylindrical, two-layered mesh, and orbital arrays. The proposed method can be used to design regular arrays with execution time of less than $<tmath>N</tmath>$ (problem size).</p><p><it>Index Terms—</it>Broadcast, cylindrical array, mesh array, orbital array, parallel algorithm design, permutation sequence, propagation, two-layered mesh array, VLSI architecture</p>