The goal of this toolbox is to provide iterative methods for sparse linear least
squares problems. This methods work with the iterative GMRES method for both
underdetermined and overdetermined problems and use various preconditionning
algorithms.
This module provides :
* AB-GMRES and BA-GMRES without any particular preconditionner,
* Robust Incomplete Factorization (RIF) preconditioning method working with
AB-GMRES and BA-GMRES,
* Greville's preconditioning method working with AB-GMRES and BA-GMRES,
* inner iterations preconditioning process with AB-GMRES and BA-GMRES.
Features
--------
* splspc_gmresab : the AB-GMRES iterative solver
* splspc_gmresba : the BA-GMRES iterative solver
* splspc_rifgmresab : the AB-GMRES iterative solver with a RIF preconditioner
* splspc_rifgmresab : the BA-GMRES iterative solver with a RIF preconditioner
* splspc_grevgmresab: the AB-GMRES iterative solver with a GREVILLE
preconditioner
* splspc_grevgmresba: the BA-GMRES iterative solver with a GREVILLE
preconditioner
* splspc_nrsorgmresba: the BA-GMRES iterative solver with an inner iteration
preconditioner
Bibliography
------------
* Hayami, K., Yin, J.-F., and Ito, T., GMRES methods for least squares
problems, SIAM Journal on Matrix Analysis and Applications, Vol. 31, Issue 5,
pp. 2400-2430, 2010.
* Hayami, K., Yin, J.-F., and Ito, T., "GMRES methods for least squares
problems", NII Technical Reports, National Institute of Informatics, Tokyo,
NII-2007-09E, pp. 1-29, July, 2007, http://www.nii.ac.jp/TechReports/07-009E.html
* Cui, X. and Hayami, K., "Greville's method for preconditioning least squares
problems",
NII Technical Reports, National Institute of Informatics, Tokyo,
NII-2008-008E, pp. 1-26, August, 2008, http://research.nii.ac.jp/TechReports/08-008E.html
* Cui, X., Hayami K., and Yin, J.-F., Greville’s method for preconditioning
least squares problems, Advances in Computational Mathematics , Vol. 35, pp.
243-269, 2011.
* Morikuni, K. and Hayami, K., Inner-iteration Krylov subspace methods for
least squares problems, NII Technical Reports, National Institute of
Informatics, Tokyo, NII-2011-001E, pp. 1-27, April, 2011. http://www.nii.ac.jp/TechReports/11-001E.html
