This paper describes an overall framework for the design of numerical libra
ries on a computational grid of processors in which the processors may be g
eographically distributed and under the control of a grid-based scheduling
system. Experiments are presented in the context of solving systems of line
ar equations using routines from the ScaLAPACK software collection along wi
th various grid service components, such as Globus, NWS, and Autopilot.