Performance analysis and optimisation of two-sided factorization algorithms for heterogeneous platform

Many applications, ranging from big data analytics to nanostructure designs, require the solution of large dense singular value decomposition (SVD) or eigenvalue problems. A first step in the solution methodology for these problems is the reduction of the matrix at hand to condensed form by two-sided orthogonal transformations. This step is standardly used to significantly accelerate the solution process. We present a performance analysis of the main two-sided factorizations used in these reductions: the bidiagonalization, tridiagonalization, and the upper Hessenberg factorizations on heterogeneous systems of multicore CPUs and Xeon Phi coprocessors. We derive a performance model and use it to guide the analysis and to evaluate performance. We develop optimized implementations for these methods that get up to 80% of the optimal performance bounds.