KrySBAS: Krylov Subspace-Based Adaptive Solvers

KrySBAS is a free and open-source MATLAB toolbox containing a collection of adaptive solvers based on Krylov subspaces.

The toolbox is developed by the Scientific Computing and Applied Mathematics group at the NIDTEC research center of the Polytechnic Faculty, National University of Asunción, Paraguay.

Installation

To install KrySBAS, simply clone this repository and add it to your MATLAB path.

Solvers catalogue

GMRES-E(m, d) (Morgan, 1995)

Modified implementation of the restarted GMRES that appends d approximate eigenvectors corresponding to a few of the smallest eigenvalues of the restarting Krylov subspace.

[x, flag, relresvec, kdvec, time] = gmres_e(A, b, m, d, tol, maxit, xInitial, eigstol)

LGMRES(m, l) (Baker & Jessup & Manteuffel, 2005)

Modified implementation of the restarted GMRES that appends l error approximation vectors to the restarting Krylov subspace as a way to preserve information from previously discarted search subspaces.

[x, flag, relresvec, kdvec, time] = lgmres(A, b, m, l, tol, maxit, xInitial)

PD-GMRES(m) (Núñez & Schaerer & Bhaya, 2018)

Variant of the restarted GMRES that employs a Proportional-Derivative (PD) controller for the automatic selection of the restart parameter m.

[x, flag, relresvec, kdvec, time] = pd_gmres(A, b, mInitial, mMinMax, mStep, tol, maxit, xInitial, alphaPD)

Contributing

If you wish to contribute to KrySBAS, please read the developer guide before opening a pull request.

Feature requests and bug reports

For future requests and bug reports, please create an issue. In the latter case, we kindly ask you to provide a MWE that reproduces the error.