Improving the Unsymmetric Parallel QR Algorithm on Vector Machines.
Greg Henry · 1993
We present some theoretical and computational improvements to the single/double shift QR algorithm on vector machines. The improvement involves a lookahead algorithm that obtains vector performance better than the high multiplicity shift QR. The strategies presented are numerically similar to those found in such libraries as LAPACK and EISPACK. We provide tests to show improved timings against LAPACK, ESSL, and the vector version of EISPACK on an IBM 3090/VF. We also provide theorems to show theoretical complexity improvements. 1 Introduction This paper examines the unsymmetric Schur decomposition for vector architectures. This method is also applicable for symmetric matrices and scalar architectures, but is most suited to finding the Schur decomposition on vector hardware. We improve the theoretical complexity of the QR approach, and reduce the overall timing. We do this by defining a lookahead or partial step. Our idea is to do the minimum amount of work possible, without ove...