9 papers · 1 filter
Contour integral methods and structured perturbations for linear differential-algebraic equations
Nicola Guglielmi, Mattia Manucci
We generalize the contour integral methods (CIM) framework to the time integration of linear dynamical systems that are subject to algebraic constraints at all times during their e…
A fast and memoryless numerical method for solving fractional differential equations
Nicola Guglielmi, Ernst Hairer
The numerical solution of implicit and stiff differential equations by implicit numerical integrators has been largely investigated and there exist many excellent efficient codes a…
Matrix nearness problems and eigenvalue optimization
Nicola Guglielmi, Christian Lubich
This book is about solving matrix nearness problems that are related to eigenvalues or singular values or pseudospectra. These problems arise in great diversity in various fields,…
Gripenberg-like algorithm for the lower spectral radius
Nicola Guglielmi, Francesco Paolo Maiale
This article presents an extended algorithm for computing the lower spectral radius of finite, non-negative matrix sets. Given a set of matrices $\mathcal{F} = \{A_1, \ldots, A_m\}…
Uniform Approximation of Eigenproblems of a Large-Scale Parameter-Dependent Hermitian Matrix
Mattia Manucci, Emre Mengi, Nicola Guglielmi
We consider the uniform approximation of the smallest eigenvalue of a large parameter-dependent Hermitian matrix by that of a smaller counterpart obtained through projections. The…
Stabilization of a matrix via a low rank-adaptive ODE
Nicola Guglielmi, Stefano Sicilia
Let be a square matrix with a given structure (e.g. real matrix, sparsity pattern, Toeplitz structure, etc.) and assume that it is unstable, i.e. at least one of its eigenvalue…
Applying stiff integrators for ODEs and DDEs to problems with distributed delays
Nicola Guglielmi, Ernst Hairer
There exist excellent codes for an efficient numerical treatment of stiff and differential-algebraic problems. Let us mention {\sc Radau5} which is based on the -stage Radau IIA…
Transient dynamics under structured perturbations: bridging unstructured and structured pseudospectra
Christian Lubich, Nicola Guglielmi
The structured -stability radius is introduced as a quantity to assess the robustness of transient bounds of solutions to linear differential equations under structure…
On the numerical approximation of the distance to singularity for matrix-valued functions
Miryam Gnazzo, Nicola Guglielmi
Given a matrix-valued function , with complex matrices and entire functions for , we discuss a method for the n…