10 papers
Neural-HSS: Hierarchical Semi-Separable Neural PDE Solver
Pietro Sittoni, Emanuele Zangrando, Angelo A. Casulli +2
Deep learning-based methods have shown remarkable effectiveness in solving PDEs, largely due to their ability to enable fast simulations once trained. However, despite the availabi…
Lanczos with compression for symmetric eigenvalue problems
Angelo A. Casulli, Daniel Kressner, Nian Shao
The Lanczos method with implicit restarting is one of the most popular methods for finding a few exterior eigenpairs of a large symmetric matrix . Usually based on polynomial fi…
Lanczos with compression for symmetric matrix Lyapunov equations
Angelo A. Casulli, Francesco Hrobat, Daniel Kressner
This work considers large-scale Lyapunov matrix equations of the form , where is a symmetric positive definite matrix and $\boldsymbol…
A low-memory Lanczos method with rational Krylov compression for matrix functions
Angelo A. Casulli, Igor Simunec
In this work we introduce a memory-efficient method for computing the action of a Hermitian matrix function on a vector. Our method consists of a rational Lanczos algorithm combine…
Computing Functions of Symmetric Hierarchically Semiseparable Matrices
Angelo A. Casulli, Daniel Kressner, Leonardo Robol
The aim of this work is to develop a fast algorithm for approximating the matrix function of a square matrix that is symmetric and has hierarchically semiseparable (HSS)…
Tensorized block rational Krylov methods for tensor Sylvester equations
Angelo Alberto Casulli
We introduce the definition of tensorized block rational Krylov subspaces and its relation with multivariate rational functions, extending the formulation of tensorized Krylov subs…
An efficient block rational Krylov solver for Sylvester equations with adaptive pole selection
Angelo A. Casulli, Leonardo Robol
We present an algorithm for the solution of Sylvester equations with right-hand side of low rank. The method is based on projection onto a block rational Krylov subspace, with two…
Low-rank tensor structure preservation in fractional operators by means of exponential sums
Angelo A. Casulli, Leonardo Robol
The use of fractional differential equations is a key tool in modeling non-local phenomena. Often, an efficient scheme for solving a linear system involving the discretization of a…
Computation of generalized matrix functions with rational Krylov methods
Angelo Alberto Casulli, Igor Simunec
We present a class of algorithms based on rational Krylov methods to compute the action of a generalized matrix function on a vector. These algorithms incorporate existing methods…
Rank-structured QR for Chebyshev rootfinding
Angelo Casulli, Leonardo Robol
We consider the computation of roots of polynomials expressed in the Chebyshev basis. We extend the QR iteration presented in [Eidelman, Y., Gemignani, L., and Gohberg, I., Numer.…