3 papers
math.NA2025
Block CG algorithms revisited
Petr Tichý, Gérard Meurant, Dorota Šimonová
Our goal in this paper is to clarify the relationship between the block Lanczos and the block conjugate gradient (BCG) algorithms. Under the full rank assumption for the block vect…
math.NA2025
Error norm estimates for the block conjugate gradient algorithm
Gérard Meurant, Petr Tichý
In the book [Meurant and Tichy, SIAM, 2024] we discussed the estimation of error norms in the conjugate gradient (CG) algorithm for solving linear systems with a symmetric p…
math.NA2024
Near-optimal convergence of the full orthogonalization method
Tyler Chen, Gérard Meurant
We establish a near-optimality guarantee for the full orthogonalization method (FOM), showing that the overall convergence of FOM is nearly as good as GMRES. In particular, we prov…