Stability Analysis and Improvement of the Block Gram-Schmidt Algorithm

The advent of supercomputers with hierarchical memory systems has imposed the use of block algorithms for the linear algebra algorithms. Although block algorithms may result in impressive improvements in performance, their numerical properties are quite different from their scalar counterpart and deserve an in-depth study. In this paper, the numerical stability ofblock Gram-Schmidt orthogonalization is studied and a variant is proposed which has numerical properties similar to the modified Gram-Schmidt procedure while retaining most of the performance advantages of the block formulation.