Automatic Parallelization of the Conjugate Gradient Algorithm

The conjugate gradient (CG) method is a popular Krylov space method for solving systems of linear equations of the form Ax = b, where A is a symmetric positive-definite matrix. This method can be applied regardless of whether A is dense or sparse. In this paper, we show how restructuring compiler technology can be applied to transform a sequential, dense matrix CG program into a parallel, sparse matrix CG program. On the IBM SP-2, the performance of our compiled code is comparable to that of handwritten code from the PETSc library at Argonne