Lyapunov equation RK solvers

Block rational Krylov subspace methods for large Lyapunov equation with a low-rank right-hand side. See readme.txt for details.

This research software package contains several numerical algorithms based on rational Krylov subspaces for approximately solving large matrix Lyapunov equation inv(M)A X + X (inv(M)A)' + Bc*Bc' = 0, where Bc is of low rank (typically <= 5). It includes the following subroutines

eksm_RX.m Extended Krylov subspace method (EKSM) by Simoncini
rksm_RX.m Adaptive rational Krylov subspace method (RKSM) by Simoncini and Druskin
feksm_RX.m Flexible EKSM by Rostami and Xue
rprksm_RX_va.m Adaptive RKSM with limited number of poles (version A)
rprksm_RX_vb.m Adaptive RKSM with limited number of poles (version B)
FindShiftCplx61.m A heuristic algorithm for finding a near-optimal pole for F-EKSM; also used by all adaptive RKSM code
script.m A script running test problems.

Note: to limit the size of the package, we only provide three sample problems. To run and compare solvers, please make changes to this script accordingly. Additional test problems are available upon request.

Authors: M. Rostami ([e-mail]) and F. Xue ([e-mail])
Version 1.0 06/08/2019

Please read the documentation in each subroutine for technical details and references.