Future computing platforms will be distributed and heterogeneous. Such platforms range from heterogeneous networks of workstations (NOWs) to collections of NOWs and parallel servers scattered throughout the world and linked through high-speed networks. Implementing tightlycoupled algorithms on such platforms raises several challenging issues. New data distribution and load balancing strategies are required to squeeze the most out of heterogeneous platforms. In this paper, we rst summarize previous results obtained for heterogeneous NOWs, dealing with the implementation of standard numerical kernels such as nite-dierence stencils or dense linear solvers. Next we target distributed collections of heterogeneous NOWs, and we discuss data allocation strategies for dense linear solvers on top of such platforms. These results indicate that a major algorithmic and software eort is needed to come up with eÆcient numerical libraries on the computational grid. Keywords: meta-computing, heter...