7 citations · 7 across the 6 of their papers we have counts for
9 papers
Efficient solution of sequences of parametrized Lyapunov equations with applications
Davide Palitta, Zoran Tomljanović, Ivica Nakić +1
Sequences of parametrized Lyapunov equations can be encountered in many application settings. Moreover, solutions of such equations are often intermediate steps of an overall proce…
On an integrated Krylov-ADI solver for large-scale Lyapunov equations
Peter Benner, Davide Palitta, Jens Saak
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 propo…
Palindromic linearization and numerical solution of nonsymmetric algebraic T-Riccati equations
Peter Benner, Bruno Iannazzo, Beatrice Meini +1
We identify a relationship between the solutions of a nonsymmetric algebraic T-Riccati equation (T-NARE) and the deflating subspaces of a palindromic matrix pencil, obtained by arr…
An efficient, memory-saving approach for the Loewner framework
Davide Palitta, Sanda Lefteriu
The Loewner framework is one of the most successful data-driven model order reduction techniques. If is the cardinality of a given data set, the so-called Loewner and shifted L…
On the Solution of the Nonsymmetric T-Riccati Equation
Peter Benner, Davide Palitta
The nonsymmetric T-Riccati equation is a quadratic matrix equation where the linear part corresponds to the so-called T-Sylvester or T-Lyapunov operator that has previously been st…
On the convergence of Krylov methods with low-rank truncations
Davide Palitta, Patrick Kürschner
Low-rank Krylov methods are one of the few options available in the literature to address the numerical solution of large-scale general linear matrix equations. These routines amou…
Matrix equation techniques for certain evolutionary partial differential equations
Davide Palitta
We show that the discrete operator stemming from the time and space discretization of evolutionary partial differential equations can be represented in terms of a single Sylvester…
Optimality properties of Galerkin and Petrov-Galerkin methods for linear matrix equations
Davide Palitta, Valeria Simoncini
Galerkin and Petrov-Galerkin methods are some of the most successful solution procedures in numerical analysis. Their popularity is mainly due to the optimality properties of their…
The projected Newton-Kleinman method for the algebraic Riccati equation
Davide Palitta
The numerical solution of the algebraic Riccati equation is a challenging task especially for very large problem dimensions. In this paper we present a new algorithm that combines…