Improving the efficiency of eigenvector-related computations

Abstract: An effective strategy in dense linear algebra is the design of algorithms as tiled algorithms. Tiled algorithms that express the bulk of the computation as matrix-matrix operations (level-3 BLAS) have proven successful in achieving high performance on cache-based architectures. At the same time, tiled algorithms interoperate with dynamic data-driven execution models such as task parallelism and promise good parallel scalability.This thesis applies the concept of tiled algorithms and task-centric execution to algorithms related to the computation of eigenvectors for the dense, non-symmetric eigenvalue problem. First, a standard algorithm for computing eigenvectors from the Schur form is recast such that all computational steps are rich in matrix-matrix operations. Second, inverse iteration on the Hessenberg matrix as an alternative approach to computing eigenvectors is addressed. An existing algorithm is revised to express the computationally most expensive step with matrix-matrix operations. Third, a task-parallel, tiled triangular Sylvester equation solver is amended to solve a larger class of problems. All algorithms have an enhanced performance, which is demonstrated through numerical experiments.