7 papers
Structured distance to singularity as a nonlinear system of equations
Miryam Gnazzo, Nicola Guglielmi, Federico Poloni +1
In this article we study the structured distance to singularity for a nonsingular matrix , with a prescribed linear structure (for instanc…
Nearest Reversible Markov Chains with Sparsity Constraints: An Optimization Approach
Stefano Cipolla, Fabio Durastante, Miryam Gnazzo +1
Reversibility is a key property of Markov chains, central to algorithms such as Metropolis-Hastings and other MCMC methods. Yet many applications yield non-reversible chains, motiv…
Kemeny's constant minimization for reversible Markov chains via structure-preserving perturbations
Fabio Durastante, Miryam Gnazzo, Beatrice Meini
Kemeny's constant measures the efficiency of a Markov chain in traversing its states. We investigate whether structure-preserving perturbations to the transition probabilities of a…
A Riemannian Optimization Approach for Finding the Nearest Reversible Markov Chain
Fabio Durastante, Miryam Gnazzo, Beatrice Meini
We address the algorithmic problem of determining the reversible Markov chain that is closest to a given Markov chain , with an identical stationary distribution. Mor…
Riemann-Oracle: A general-purpose Riemannian optimizer to solve nearness problems in matrix theory
Miryam Gnazzo, Vanni Noferini, Lauri Nyman +1
We propose an extremely versatile approach to address a large family of matrix nearness problems, possibly with additional linear constraints. Our method is based on splitting a ma…
Backward errors for multiple eigenpairs in structured and unstructured nonlinear eigenvalue problems
Miryam Gnazzo, Leonardo Robol
Given a nonlinear matrix-valued function and approximate eigenpairs , we discuss how to determine the smallest perturbation such that $[F + δF](λ_i) v_i = 0…