A posteriori superlinear convergence bounds for block conjugate gradient
Numerical Analysis
2022-09-13 v3 Numerical Analysis
Abstract
In this paper, we extend to the block case, the a posteriori bound showing superlinear convergence of Conjugate Gradients developed in [J. Comput. Applied Math., 48 (1993), pp. 327-341]; that is, we obtain similar bounds, but now for block Conjugate Gradients. We also present a series of computational experiments illustrating the validity of the bound developed here, as well as the bound from [SIAM Review, 47 (2005), pp. 247-272] using angles between subspaces. Using these bounds, we make some observations on the onset of superlinearity, and how this onset depends on the eigenvalue distribution and the block size.
Keywords
Cite
@article{arxiv.2107.10320,
title = {A posteriori superlinear convergence bounds for block conjugate gradient},
author = {Christian E. Schaerer and Daniel B. Szyld and Pedro J. Torres},
journal= {arXiv preprint arXiv:2107.10320},
year = {2022}
}
Comments
21 pages, 14 figures