The preconditioned conjugate gradient method on the connection machine.

*(English)*Zbl 0725.65033This is a report on numerical experiments where more than ten preconditioners were compared in their performance on a quarter of the connection machine (which means \(2^{14}\) processors, connected in hypercube mode). The problem is the solution of the 5-point approximation to the Poisson and the anisotropic Poisson equation in the unit square; by computing time the simple 4-step Jacobi preconditioner turned out to be best. Interestingly, the unpreconditioned conjugate gradient method needed less than twice as much time.

There is a broad discussion of several aspects of the experiments, and a list of computing times measured for basic arithmetical operations (showing rather unexpected time relations, from a sequential point of view).

There is a broad discussion of several aspects of the experiments, and a list of computing times measured for basic arithmetical operations (showing rather unexpected time relations, from a sequential point of view).

Reviewer: G.Stoyan (Budapest)

##### MSC:

65F10 | Iterative numerical methods for linear systems |

65F35 | Numerical computation of matrix norms, conditioning, scaling |

65N22 | Numerical solution of discretized equations for boundary value problems involving PDEs |

65Y05 | Parallel numerical computation |

65N06 | Finite difference methods for boundary value problems involving PDEs |

35J25 | Boundary value problems for second-order elliptic equations |