Adaptive Parallel Householder Bidiagonalization

With the increasing use of high-resolution multimedia streams and large image and video archives in many of today’s research and application areas, there is a growing need for multimedia-oriented highperformance computing. As a consequence, a need for algorithms, methodologies, and tools that can serve as support in the (automatic) parallelization of multimedia applications is rapidly emerging. This paper discusses the parallelization of Householder bidiagonalization, a matrix factorization method which is an integral part of full Singular Value Decomposition (SVD) — an important algorithm for many multimedia problems. Householder bidiagonalization is hard to parallelize efficiently because the total number of matrix elements taking part in the calculations reduces during runtime. To overcome the growing negative performance impact of load imbalances and overprovisioning of compute resources, we apply adaptive runtime techniques of periodic matrix remapping and process reduction for improved performance. Our results show that, with our approach, we have arrived at a solution for parallel Householder bidiagonalization that obtains high speedups, even when applying a set of compute resources which is (initially) very large.