In this paper we present a performance evaluation of large scale matrix algebra applications on the Grid'5000 platform. Grid'5000 is a nation wide experimental set of clusters which provide a reconfigurable and highly controllable and monitorable instrument. We test the scalability of the experimental tool and some optimization techniques for large scale matrix algebra applications in grid infrastructures based on an efficient data locality, already presented for non-dedicated grid platforms. This includes persistent data placement and explicit management of local memories on the computational nodes. We discuss the performances of a block-based matrix-vector product and the Gauss-Jordan method for large matrix inversion. As experimental grid middleware we use the XtremWeb system to manage the Grid'5000 computational resources. We also compare these results with those obtained on large non-dedicated computational platforms distributed on two geographic sites in France and Japan, we show the effectiveness of the presented data placement techniques but that some constraints and limitations on the experimentation and underlying tools make scalability and realistic expectations more difficult