Stationary biparametric ADI preconditioners for conjugate gradient methods

Parallelization Properties of Preconditioners for the Conjugate Gradient Methods

In this paper we present the analysis of parallelization properties of several typical preconditioners for the Conjugate Gradient methods. For implicit preconditioners, geometric and algebraic parallelization approaches are discussed. Additionally, different optimization techniques are suggested. Some implementation details are given for each method. Finally, parallel performance results are pr...

Optimal Alternating Direction Implicit Preconditioners for Conjugate Gradient methods

The (Extrapolated) Alternating Direction Implicit Preconditioners for the class of Conjugate Gradient Methods are applied for the solution of the second order elliptic equation in a rectangle under Dirichlet boundary conditions. The PDE is approximated by uniform meshes of 5− and 9−point difference schemes and analytic expressions for the optimal acceleration and extrapolation parameters are ob...

Preconditioners for the conjugate gradient algorithm using Gram-Schmidt and least squares methods

This paper is devoted to the study of some preconditioners for the conjugate gradient algorithm used to solve large sparse linear and symmetric positive definite systems. The construction of a preconditioner based on the Gram–Schmidt orthogonalization process and the least squares method is presented. Some results on the condition number of the preconditioned system are provided. Finally, numer...

On Conjugate Gradient Type Methods and Polynomial Preconditioners for a Class of Complex Non-Hermitian Matrices

Novel preconditioners based on quasi-Newton updates for nonlinear conjugate gradient methods

In this paper we study new preconditioners to be used within the Nonlinear Conjugate Gradient (NCG) method, for large scale unconstrained optimization. The rationale behind our proposal draws inspiration from quasi– Newton updates, and its aim is to possibly approximate in some sense the inverse of the Hessian matrix. In particular, at the current iteration of the NCG we consider some precondit...