On the estimation of a large sparse Bayesian system: The Snaer program
Computational Statistics & Data Analysis
Preconditioning and convergence in the right norm
International Journal of Computer Mathematics - Fast Iterative and Preconditioning Methods for Linear and Non-Linear Systems
From Functional Analysis to Iterative Methods
SIAM Review
A Posteriori Error Estimates Including Algebraic Error and Stopping Criteria for Iterative Solvers
SIAM Journal on Scientific Computing
Fast Algorithms for Source Identification Problems with Elliptic PDE Constraints
SIAM Journal on Imaging Sciences
On Efficient Numerical Approximation of the Bilinear Form $c^*A^{-1}b$
SIAM Journal on Scientific Computing
VECPAR'04 Proceedings of the 6th international conference on High Performance Computing for Computational Science
Solving Hermitian positive definite systems using indefinite incomplete factorizations
Journal of Computational and Applied Mathematics
Computational Optimization and Applications
Interactive topology optimization on hand-held devices
Structural and Multidisciplinary Optimization
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The Conjugate Gradient method has always been successfully used in solving the symmetric and positive definite systems obtained by the finite element approximation of self-adjoint elliptic partial differential equations. Taking into account recent results [13, 19, 20, 22] which make it possible to approximate the energy norm of the error during the conjugate gradient iterative process, we adapt the stopping criterion introduced in [3]. Moreover, we show that the use of efficient preconditioners does not require to change the energy norm used by the stopping criterion. Finally, we present the results of several numerical tests that experimentally validate the effectiveness of our stopping criterion.