<p><it>Abstract—</it>In this paper, we present some new regular iterative algorithms for matrix multiplication and transitive closure. With these algorithms, by spacetime mapping the 2-D arrays with $<tmath>2N - 1</tmath>$ and $<tmath>\lceil (3N - 1)/2\rceil</tmath>$ execution times for matrix multiplication can be obtained. Meanwhile, we can derive a 2-D array with $<tmath>4N - 2</tmath>$ execution time for transitive closure based on the sequential Warshall-Floyd algorithm. All these new 2-D arrays for matrix multiplication and transitive closure have the advantages of faster and more regular than other previous designs.</p><p><it>Index Terms—</it>Algorithm mapping, matrix multiplication, mesh array, systolic array, spherical array, transitive closure, VLSI architecture.</p>