The Application of Projected Conjugate Gradient Solvers on Graphical Processing Units

Graphical processing units introduce the capability for large scale computation in the desk top environment. For the solution of linear systems of equations, much effort has been devoted to efficient implementation of Krylov subspace-based solvers in high performance computing environments. Here the focus is to improve the computational efficiency of the projected conjugate gradient algorithm. Although the current graphical processing unit architectures are better suited to single precision accuracy, the projected conjugate gradient algorithm can still be used. The projected conjugate gradient is implemented using block operations, hence optimizing the usage of basic linear algebra subroutines of level 3, and further improving the graphical processing unit implementation. Numerical results using the graphical processing unit are provided to support the proposed algorithm for the reconstruction of consecutive slices of a three dimensional Shepp-Logan phantom.