Block conjugate gradient type methods for the approximation of bilinear form CHA−1B

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...

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...

Multigrid-Conjugate Gradient Type Methods for Reaction-diffusion Systems

We study multigrid methods in the context of continuation methods for reaction–diffusion systems, where the Bi-CGSTAB and GMRES methods are used as the relaxation scheme for the V-cycle, W-cycle and full approximation schemes, respectively. In particular, we apply the results of Brown and Walker [1997] to investigate how the GMRES method can be used to solve nearly singular systems that occur i...

On a Variable Smoothing Procedure for Conjugate Gradient Type Methods

The smoothing procedure has been introduced by Schh onauer as an acceleration algorithm for the Generalized Conjugate Gradient methods. In this paper, after giving our deenition of Conjugate Gradient type methods, and using a Generalized Hessenberg process, we introduce a Hybrid generalized Conjugate Gradient type method. We show that this Hybrid procedure is a variable smoothing procedure. And...

Multilevel Conjugate Gradient Methods