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Matrix equations of the kind A(1)X(2)+A(0)X+A(-1)=X, where both the matrix coefficients and the unknown are semi-infinite matrices belonging to a Banach algebra, are considered. These equations, where coefficients are quasi-Toeplitz matrices, are encounter ...
In this work, we consider two types of large-scale quadratic matrix equations: Continuous-time algebraic Riccati equations, which play a central role in optimal and robust control, and unilateral quadratic matrix equations, which arise from stochastic proc ...
Evaluating the action of a matrix function on a vector, that is x=f(M)v, is an ubiquitous task in applications. When M is large, one usually relies on Krylov projection methods. In this paper, we provide effective choices for the pole ...
We consider the problem of efficiently solving Sylvester and Lyapunov equations of medium and large scale, in case of rank-structured data, i.e., when the coefficient matrices and the right-hand side have low-rank off-diagonal blocks. This comprises proble ...
We consider the discretization of time-space diffusion equations with fractional derivatives in space and either 1D or 2D spatial domains. The use of implicit Euler scheme in time and finite differences or finite elements in space, leads to a sequence of d ...
A Quasi Toeplitz (QT) matrix is a semi-infinite matrix of the kind A=T(a)+E whereT(a)=(aj−i)i,j∈Z+, E=(ei,j)i,j∈Z+ is compact and the norms ∥a∥W=∑i∈Z∣a∣j and $|E|_{ ...
We consider the problem of efficiently solving Sylvester and Lyapunov equations of medium and large scale, in case of rank-structured data, i.e., when the coefficient matrices and the right-hand side have low-rank off- diagonal blocks. This comprises probl ...
Linear matrix equations, such as the Sylvester and Lyapunov equations, play an important role in various applications, including the stability analysis and dimensionality reduction of linear dynamical control systems and the solution of partial differentia ...
