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. ...

We propose a novel variant of the conjugate gradient algorithm, Kernel Conjugate Gradient (KCG), designed to speed up learning for kernel machines with differentiable loss functions. This approach leads to a better conditioned optimization problem during learning. We establish an upper bound on the number of iterations for KCG that indicates it should require less than the square root of the nu...

Partial spectral information associated with the smallest eigenvalues can be used to improve the solution of successive linear systems of equations, namely in the simulation of time-dependent partial differential equations, where at each time step there are several systems with the same spectral properties to be solved. We propose to perform a partial spectral decomposition with the BlockCGSI a...