Parallel Svd Computation in Updating Problems of Latent Semantic Indexing ∗

In latent semantic indexing, the addition of documents (or the addition of terms) to some already processed text collection leads to the updating of the best rank-k approximation of the term-document matrix. The computationally most intensive task in this updating is the computation of the singular value decomposition (SVD) of certain square matrix, which is upper or lower triangular, and contains a diagonal block in its upper left corner. For the solution of this task, the new dynamic ordering of subproblems is compared with the up-to-now preferred static cyclic one in the parallel two-sided block-Jacobi SVD algorithm. The results of numerical experiments show that, for a given accuracy, the dynamic ordering is much more efficient that the static cyclic one with respect to the number of parallel iteration steps needed for the convergence of the two-sided block-Jacobi SVD algorithm.