Conjugate gradient (CG) and biconjugate gradient stabilized (BiCGSTAB) are effective
methods used for solving sparse linear systems. We in this paper propose Mille-feuille, a …

Matrix functions are a central topic of linear algebra, and problems requiring their numerical
approximation appear increasingly often in scientific computing. We review various limited …

One of the most computationally expensive steps of the low-rank ADI method for large-scale
Lyapunov equations is the solution of a shifted linear system at each iteration. We propose …

Thanks to its great potential in reducing both computational cost and memory requirements,
combining sketching and Krylov subspace techniques has attracted a lot of attention in the …

Thanks to its great potential in reducing both computational cost and memory requirements,
combining sketching and Krylov subspace techniques has attracted a lot of attention in the …

We derive the alternating-directions implicit (ADI) method based on a commuting operator
split and apply the results in detail to the continuous time algebraic Lyapunov equation with …

Sequences of parametrized Lyapunov equations can be encountered in many application
settings. Moreover, solutions of such equations are often intermediate steps of an overall …

We derive the Alternating-Direction Implicit (ADI) method based on a commuting operator
split and apply the results to the continuous time algebraic Lyapunov equation with low-rank …

Of all the possible projection methods for solving large-scale Lyapunov matrix equations,
Galerkin approaches remain much more popular than minimal-residual ones. This is mainly …

We consider the low-rank alternating directions implicit (ADI) iteration for approximately
solving large-scale algebraic Sylvester equations. Inside every iteration step of this iterative …