Zobrazeno 1 - 10
of 163
pro vyhledávání: '"Robol, Leonardo"'
In the last decade, tensors have shown their potential as valuable tools for various tasks in numerical linear algebra. While most of the research has been focusing on how to compress a given tensor in order to maintain information as well as reducin
Externí odkaz:
http://arxiv.org/abs/2409.09471
This work is concerned with the numerical solution of large-scale symmetric positive definite matrix equations of the form $A_1XB_1^\top + A_2XB_2^\top + \dots + A_\ell X B_\ell^\top = F$, as they arise from discretized partial differential equations
Externí odkaz:
http://arxiv.org/abs/2408.16416
Backward errors for multiple eigenpairs in structured and unstructured nonlinear eigenvalue problems
Autor:
Gnazzo, Miryam, Robol, Leonardo
Given a nonlinear matrix-valued function $F(\lambda)$ and approximate eigenpairs $(\lambda_i, v_i)$, we discuss how to determine the smallest perturbation $\delta F$ such that $[F + \delta F](\lambda_i) v_i = 0$; we call the distance between the $F$
Externí odkaz:
http://arxiv.org/abs/2405.06327
The aim of this work is to develop a fast algorithm for approximating the matrix function $f(A)$ of a square matrix $A$ that is symmetric and has hierarchically semiseparable (HSS) structure. Appearing in a wide variety of applications, often in the
Externí odkaz:
http://arxiv.org/abs/2402.17369
Autor:
Bucci, Alberto, Robol, Leonardo
The Nystr\"om method offers an effective way to obtain low-rank approximation of SPD matrices, and has been recently extended and analyzed to nonsymmetric matrices (leading to the generalized Nystr\"om method). It is a randomized, single-pass, stream
Externí odkaz:
http://arxiv.org/abs/2309.02877
Autor:
Casulli, Angelo A., Robol, Leonardo
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 key contributions with respect to the state-of-the-art. First, we show
Externí odkaz:
http://arxiv.org/abs/2301.08103
Autor:
Massei, Stefano, Robol, Leonardo
Linear systems with a tensor product structure arise naturally when considering the discretization of Laplace type differential equations or, more generally, multidimensional operators with separable coefficients. In this work, we focus on the numeri
Externí odkaz:
http://arxiv.org/abs/2301.06781
Autor:
Casulli, Angelo A., Robol, Leonardo
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 fractional operator is evaluating the matrix function $x = \mathcal A
Externí odkaz:
http://arxiv.org/abs/2208.05189
Tropical roots of tropical polynomials have been previously studied and used to localize roots of classical polynomials and eigenvalues of matrix polynomials. We extend the theory of tropical roots from tropical polynomials to tropical Laurent series
Externí odkaz:
http://arxiv.org/abs/2107.07982
A novel compressed matrix format is proposed that combines an adaptive hierarchical partitioning of the matrix with low-rank approximation. One typical application is the approximation of discretized functions on rectangular domains; the flexibility
Externí odkaz:
http://arxiv.org/abs/2104.11456