The availability of powerful computers and high-speed network technologies has changed the way of using computers in the last decade. A number of scientific applications that have traditionally performed on supercomputers run on a variety of heterogeneous resources geographically distributed. Peer-to-Peer (P2P) global computing paradigm for large scale scientific applications is emerging as a new solution. Peer-to-Peer global computing platforms enable the sharing, selection, and aggregation of a wide variety of heterogeneous resources geographically distributed, such as computers and data sources, to solve large-scale problems in science, engineering and commerce, which cannot be effectively dealt using the current generation of supercomputers or which are less expensive or accessible with this approach. In a peer-to-peer architecture, computers that have traditionally been used alone as clients communicate directly among themselves and can act as both clients and servers. It takes advantage of existing computing power and networking connectivity, allowing users to leverage their collective power to benefit other users that need them. Many applications might be amenable to this approach, including collaborative engineering, medical data exchange and analysis, data exploration and mining, high-throughput computing and distributed supercomputing. However, parallel and distributed application developments and resource managements in these environments are a new and complex undertaking. In scientific computation, the validity of calculations, the numerical stability, the choices of methods and software's are depending of properties of each peer and its software and hardware environments; which are known only at run time and are indeterminists. In this talk, we will focus on large scale parallel matrix computing experimentations on such environments. We will present experimental results for several basic linear algebra methods such as the matrix-vector products, linear system solving (Block Gauss-Jordan) and eigenvalue approximations (Givens-Householder). We will explain how we adapted parallel methods for P2P platforms and we will present performance evaluations with respect to several parameters. A comparison with out-of-core global computing approaches will be also discussed. These results are obtained using a large P2P platform running with the XtremWeb, XtremWeb-CH or OmniRPC middlewares on different interconnected experimental platforms located in France and Japan. Then, we will first conclude that the P2P matrix computing has, at least, to use more sophisticated scheduling strategies and middlewares to be propose to end users. Even if this case, only a short class of matrix methods seems to be well-adapted to this programming paradigm with the present technologies. We will discuss the limits of the P2P Parallel Matrix Computing and conclude that it would be possible to obtain, in a close future, important P2P methods to solve some large scale numerical problems if we are able to select well-adapted methods and if we can introduce pertinent and accurate economic and evaluation models. We will propose research perspectives to reach this goal.

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