An iterative solver benchmark

In scientific computing, several benchmarks exist that give a user some idea of the to-be-expected performance given a code and a specific computer. One widely accepted performance measurement is the Linpack benchmark [4], which evaluates the efficiency with which a machine can solve a dense system of equations. Since this operation allows for considerable reuse of data, it is possible to show performance figures that are a sizeable percentage of peak performance, even for machines with a severe imbalance between memory and processor speed. However, sparse linear systems are at least as important in scientific computing, and for these the question of data reuse is more complicated. Sparse systems can be solved by direct or iterative methods, and especially for iterative methods one can say that there is little or no reuse of data. Thus, such operations will have a performance bound by the slower of the processor and the memory, in practice: the memory. We aim to measure the performance of a representative sample of iterative techniques on any given machine; we are not interested in comparing, say, one preconditioner on one machine against another preconditioner on another machine. In fact, the range of possible preconditioners is so large, and their performance so much dependent on the specific problem, that we do