Ponente
Descripción
In many applications arising in scientific computing one has to solve a linear system of the type $\mathit{A}\mathbf{x} = \mathbf{b}$, where $A$ is a square, often non-symmetric and potentially ill-conditioned matrix, $\mathbf{x}$ is the unknown solution and $\mathbf{b}$ is a vector with known data. For systems with large $A$ $(>10^{5})$, it is not feasible to use direct solvers due to computational limitations and one therefore employs indirect solvers. Among them, there is a family of solvers based on Krylov subspaces. Unfortunately, using traditional solvers such as GMRES or the restarted version GMRES($m$) might result in low convergence at best or stagnation at worst. One alternative is to employ solvers that can adaptively change the restart parameter $m$ or enrich the Krylov subspace. Notably, many of these solvers are currently not available to the scientific computing community. We were therefore motivated to develop KrySBAS, an open-source software written for MATLAB/OCTAVE containing a collection of adaptive solvers based on Krylov subspaces. KrySBAS is open-source and freely available at www.github.com/nidtec-una/krysbas-dev.
The most recent version KrySBAS v0.3.0 contains the following solvers: (i) PD-GMRES, a variant of GMRES($m$) that employs a proportional-derivative controller for the automatic selection of the restart parameter $m$, (ii) LGMRES, a modified implementation of the GMRES($m$) that appends $k$ error approximation vectors to the restarting Krylov subspace as a way to preserve information from previously discarded search subspaces, and (iii) GMRES-E, a modified implementation of the GMRES($m$), performed by appending $d$ eigenvectors corresponding to the harmonic Ritz vectors associated to the harmonic Ritz values per outer iteration. KrySBAS is thoroughly tested with unit and functional tests using MOxUnit within automated workflows. Metrics for test coverage are automatically generated by MOxCov and CodeCov. Documentation of the package is generated using Sphinx and available through readthedocs.
Funding: JV is funded by the Paraguayan National Council of Science and Technology (CONACYT) through the Advanced Human Capital Insertion Program in Academia PRIA01-8. GE was funded by CONACYT through the Incentive for the Training of Researchers in National Postgraduate Programs.
