The block conjugate gradient algorithm and related methods

Application of frames in Chebyshev and conjugate gradient methods

‎Given a frame of a separable Hilbert space $H$‎, ‎we present some‎ ‎iterative methods for solving an operator equation $Lu=f$‎, ‎where $L$ is a bounded‎, ‎invertible and symmetric‎ ‎operator on $H$‎. ‎We present some algorithms‎ ‎based on the knowledge of frame bounds‎, ‎Chebyshev method and conjugate gradient method‎, ‎in order to give some‎ ‎approximated solutions to the problem‎. ‎Then we i...

Vectorization of some block preconditioned conjugate gradient methods

The block preconditioned conjugate gradient methods are very effective to solve the linear systems arising from the discretization of elliptic PDE. Nevertheless, the solution of the linear system Ms = r, to get the preconditioned residual, is a 'bottleneck', on vector processors. In this paper, we show how to modify the algorithm, in order to get better performances, on such computers. Numerica...

Multilevel Conjugate Gradient Methods

An Efficient Conjugate Gradient Algorithm for Unconstrained Optimization Problems

In this paper, an efficient conjugate gradient method for unconstrained optimization is introduced. Parameters of the method are obtained by solving an optimization problem, and using a variant of the modified secant condition. The new conjugate gradient parameter benefits from function information as well as gradient information in each iteration. The proposed method has global convergence und...

Extensions of the Hestenes-Stiefel and Polak-Ribiere-Polyak conjugate gradient methods with sufficient descent property

Using search directions of a recent class of three--term conjugate gradient methods, modified versions of the Hestenes-Stiefel and Polak-Ribiere-Polyak methods are proposed which satisfy the sufficient descent condition. The methods are shown to be globally convergent when the line search fulfills the (strong) Wolfe conditions. Numerical experiments are done on a set of CUTEr unconstrained opti...