Numerical Experiments with the Lagrange Multiplier and Conjugate Gradient Methods (ILMCGM)

Conjugate-Gradient Preconditioning Methods: Numerical Results

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...

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...

Multilevel Conjugate Gradient Methods

Optimized Schwarz and 2-lagrange Multiplier Methods for Multiscale Pdes

In this article, we formulate and analyze a two-level preconditioner for Optimized Schwarz and 2-Lagrange Multiplier methods for PDEs with highly heterogeneous (multiscale) diffusion coefficients. The preconditioner is equipped with an automatic coarse space consisting of low-frequency modes of the subdomain Dirichlet-to-Neumann maps. Under a suitable change of basis, the preconditioner is a 2 ...