14 papers · 1 filter
Error formulas for block rational Krylov approximations of matrix functions
Stefano Massei, Leonardo Robol
This paper investigates explicit expressions for the error associated with the block rational Krylov approximation of matrix functions. Two formulas are proposed, both derived from…
On the data-sparsity of the solution of Riccati equations with applications to feedback control
Stefano Massei, Luca Saluzzi
Solving large-scale continuous-time algebraic Riccati equations is a significant challenge in various control theory applications. This work demonstrates that when the matrix coeff…
Optimal Polynomial Smoothers for Parallel AMG
Pasqua D'Ambra, Fabio Durastante, Salvatore Filippone +2
In this paper, we explore polynomial accelerators that are well-suited for parallel computations, specifically as smoothers in Algebraic MultiGrid (AMG) preconditioners. These acce…
Divide and conquer methods for functions of matrices with banded or hierarchical low-rank structure
Alice Cortinovis, Daniel Kressner, Stefano Massei
This work is concerned with approximating matrix functions for banded matrices, hierarchically semiseparable matrices, and related structures. We develop a new divide-and-conquer m…
Hierarchical adaptive low-rank format with applications to discretized PDEs
Stefano Massei, Leonardo Robol, Daniel Kressner
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 approxima…
Mixed precision recursive block diagonalization for bivariate functions of matrices
Stefano Massei, Leonardo Robol
Various numerical linear algebra problems can be formulated as evaluating bivariate function of matrices. The most notable examples are the Fréchet derivative along a direction, th…