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  • SKSM_cTri: Enhanced standard Krylov subspace method for symmetric Lyapunov equations

These Matlab codes iteratively solve large-scale Sylvester and Lyapunov matrix equations with symmetric coeff. matrix by means of the standard Krylov method with Galerkin condition (low CPU and memory requirements).

Related manuscript:

D. Palitta and Valeria Simoncini, Computationally enhanced projection methods for symmetric Sylvester and Lyapunov matrix equations.


  • EKSM_genSylv_LRcomm: Extended Krylov Subspace Method for generalized Sylvester equations with low-rank commuting coefficients

This Matlab code iteratively solves large-scale generalized Sylvester and Lyapunov matrix equations with low-rank commuting coefficients by means of the extended Krylov method and a proper selection of the starting blocks.

Related manuscript:

Elias Jarlebring, Giampaolo Mele, D. Palitta and Emil Ringh, Krylov methods for low-rank commuting generalized Sylvester equations.


  • hm-toolbox: Matlab Toolbox implementing H-matrices arithmetic. It includes routines for solving large-scale Lyapunov and Sylvester matrix equations with quasiseparable data.

Related manuscript:

Stefano Massei, D. Palitta and Leonardo Robol, Solving rank structured Sylvester and Lyapunov equations.


  • lyap_banded: Efficient solution of large-scale Lyapunov equation with symmetric banded data

This Matlab code solves a large-scale Lyapunov matrix equation with SPD banded ill-conditioned coeff. matrix and banded right-hand side by the algorith called lyap_banded.

Related manuscript:

D. Palitta and Valeria Simoncini, Numerical methods for large-scale Lyapunov equation with symmetric banded data.