Parallel and distributed programming for large scale computing platforms is a topical and challenging issue. Through our experience on the distribution and parallelization of linear algebra problems, especially the real symmetric eigenproblem, we present in this Chapter our approach to tackle this issue. It starts from very early choices related to numerical algorithms in order to determine an optimal communication paradigm. As an example, by choosing the Bisection algorithm, we underline how far is interesting the parametric-parallelism paradigm in the context of world-wide computing. We also emphasize the importance of data distribution on communication and we propose useful techniques to deploy an application on a web-based heterogeneous environment. In particular, out-of-core programming and data persistence are relevant in this context. We evaluate our case study application on nation and world-wide platforms by using the XtremWeb peer-to-peer middleware and the OmniRPC grid computing middleware. In addition, we perform evaluations on large size instances of the eigenproblem. Therefore, we show the feasibility of the global computing model for linear algebra problems.
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