A stopping criterion for the conjugate gradient algorithm in the framework of anisotropic adaptive finite elements

Stopping criteria for Krylov methods and finite-element approximation of variational problems

We combine linear algebra techniques with finite element techniques to obtain a reliable stopping cri-terion for Krylov method based algorithms. The Conjugate Gradient method has for a long time beensuccessfully used in the solution of the symmetric and positive definite systems obtained from thefinite-element approximation of self-adjoint elliptic partial differential equations...

A Stopping Criterion for the Conjugate Gradient Algorithm ina Finite Element Method

Stopping Criteria for Adaptive Finite Element Solvers

We consider a family of practical stopping criteria for linear solvers for adaptive finite element methods for symmetric elliptic problems. A contraction property between two consecutive levels of refinement of the adaptive algorithm is shown when the a family of smallness criteria for the corresponding linear solver residuals are assumed on each level or refinement. More importantly, based on ...

A Note on the Descent Property Theorem for the Hybrid Conjugate Gradient Algorithm CCOMB Proposed by Andrei

In [1] (Hybrid Conjugate Gradient Algorithm for Unconstrained Optimization J. Optimization. Theory Appl. 141 (2009) 249 - 264), an efficient hybrid conjugate gradient algorithm, the CCOMB algorithm is proposed for solving unconstrained optimization problems. However, the proof of Theorem 2.1 in [1] is incorrect due to an erroneous inequality which used to indicate the descent property for the s...

A Three-terms Conjugate Gradient Algorithm for Solving Large-Scale Systems of Nonlinear Equations

Nonlinear conjugate gradient method is well known in solving large-scale unconstrained optimization problems due to it’s low storage requirement and simple to implement. Research activities on it’s application to handle higher dimensional systems of nonlinear equations are just beginning. This paper presents a Threeterm Conjugate Gradient algorithm for solving Large-Scale systems of nonlinear e...