Matlab code for the solution of tensor Sylvester equations employing Tensor block rational Krylov methods.
The algorithms contained in this repository are described in [1].
To run codes in MATLAB the packages RKTooblox and TT-Toolbox described in [2] and [3], respectively, are needed.
The main algorithms are "Tuck_Sylvester_adaptive" and "TT_Sylvester_adaptive" which can be used for the resolution of tensor Sylvester equation with right-hand side in Tucker and tensor train format, respectively.
The repository "experiments" contains the code to reproduce all the numerical experiments from the preprint [1].
-- Correspondence between scripts and figures/tables in the paper --
tuck_example_symm_d4 -> Figure 1a
tuck_example_nonsymm_d3-> Figure 1b
tuck_table_nonsymm_d3 -> Table 1
tuck_example_symm_Incr_n -> Figure 2
TT_example_symm_d6 -> Figure 3a
tt_example_nonsymm_d5 -> Figure 3b
TT_example_symm_d6_Incr_n -> Figure 4
tt_example_amen -> Table 2
tt_example_increasing_d -> Table 3
[1] Casulli, A., Tensorized block rational Krylov methods for tensor Sylvester equations.
[2] Mario Berljafa, Steven Elsworth, and Stefan Güttel. A rational Krylov toolbox for matlab. 2014.
[3] IV Oseledets et al. TT-Toolbox software; see https://github.com/oseledets.