Improving data locality of the nonsymmetric QR algorithm

The QR algorithm computes the Schur decomposition of a matrix and is the most popular algorithm for solving eigenvalue problems for dense nonsymmetric matrices. The algorithm suffers from a memory access bottleneck though. By restructuring the application of Householder reflectors to the transformation matrix in the nonsymmetric QR algorithm, data locality can be improved, increasing performance. This improvement is demonstrated against the LAPACK implementation of the implicit QR algorithm for nonsymmetric matrices, DLAHQR.