New step lengths in conjugate gradient 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...

Multilevel Conjugate Gradient Methods

An K - Step Preconditioned Conjugate Gradient Hethod

Tbis paper describes a preconditioned conjugate gradient method tbat can be effectively implemented on both vector machines and parallel arrays to solve sparse symmetric and positive definite systema of linear equations. The implementation on the CYBER 203/205 and on tbe Finite Element Machine is discuased and result a obtained using the method on these machines are siven.

The Adaptive s-step Conjugate Gradient Method

On modern large-scale parallel computers, the performance of Krylov subspace iterative methods is limited by global synchronization. This has inspired the development of s-step (or communication-avoiding) Krylov subspace method variants, in which iterations are computed in blocks of s. This reformulation can reduce the number of global synchronizations per iteration by a factor of O(s), and has...

Variable Metric Conjugate Gradient Methods