Beyond massive parallelism: numerical computation using associative tables

Novel computing devices are exploited for numerical computation. The solution of a numerical problem is sought, which has been solved many times before, but this time with a di erent set of input data. A table is a classical way to collect the old solutions in order to exploit them to nd the new one. This process is extended to more general problems than the usual function value approximation. To do this, a new concept of table is introduced. These tables are addressed associatively. Several problems are treated both theoretically and computationally. These problems include solving linear systems of equations, partial di erential equations, nonlinear systems of ordinary di erential equations, and Karmarkar's algorithm. Hardware requirements are discussed. AMS(MOS) subject classi cations. 65W05, 65F10, 65N10