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.

Analysis of computing open source systems

Graphical user interfaces (GUIs) are critical components of today's open source software. Given their increased relevance, the correctness and usability of GUIs are becoming essential. This paper describes the latest results in the development of our tool to reverse engineer the GUI layer of interactive computing open source systems. We use static analysis techniques to generate models of the user interface behavior from source code. Models help in graphical user interface inspection by allowing designers to concentrate on its more important aspects. One particular type of model that the tool is able to generate is state machines. The paper shows how graph theory can be useful when applied to these models. A number of metrics and algorithms are used in the analysis of aspects of the user interface's quality. The ultimate goal of the tool is to enable analysis of interactive system through GUIs source code inspection.