This paper models data use in the Unsymmetric QR Eigenvalue Algorithm to improve performance on machines with memory hierarchy. Most of the algorithms and strategies presented can be implemented so that they are numerically similar to strategies found in such libraries as LAPACK and EISPACK ([1,5]). We provide tests to show improvement of performance. Some strategies implemented include the use of block methods, transposing the matrix, reducing the average stride, reducing data movement with hybrid steps, and using block data structures.