Eigenvalue computations in the context of data-sparse approximations of integral operators

In this work, we consider the numerical solution of a large eigenvalue problem resulting from a finite rank discretization of an integral operator. We are interested in computing a few eigenpairs, with an iterative method, so a matrix representation that allows for fast matrix-vector products is required. Hierarchical matrices are appropriate for this setting, and also provide cheap LU decompositions required in the spectral transformation technique. We illustrate the use of freely available software tools to address the problem, in particular SLEPc for the eigensolvers and HLib for the construction of H-matrices. The numerical tests are performed using an astrophysics application. Results show the benefits of the data-sparse representation compared to standard storage schemes, in terms of computational cost as well as memory requirements.

Integration of Standardized Management Systems: A Dilemma?

Abstract: The growing proliferation of management systems standards (MSSs), and their individualized implementation, is a real problem faced by organizations. On the other hand, MSSs are aimed at improving efficiency and effectiveness of organizational responses in order to satisfy the requirements, needs and expectations of the stakeholders. Each organization has its own identity and this is an issue that cannot be neglected; hence, two possible approaches can be attended. First, continue with the implementation of individualized management systems (MSs); or, integrate the several MSSs versus related MSs into an integrated management system (IMS). Therefore, in this context, organizations are faced with a dilemma, as a result of the increasing proliferation and diversity of MSSs. This paper takes into account the knowledge gained through a case study conducted in the context of a Portuguese company and unveils some of the advantages and disadvantages of integration. A methodology is also proposed and presented to support organizations in developing and structuring the integration process of their individualized MSs, and consequently minimize problems that are generators of inefficiencies, value destruction and loss of competitiveness. The obtained results provide relevant information that can support Top Management decision in solving that dilemma and consequently promote a successful integration, including a better control of business risks associated to MSSs requirements and enhancing sustainable performance, considering the context in which organizations operate.