4 papers · 1 filter
Simultaneous Global Convergence Failure of Newton's and Halley's Methods in Degree Four
Alessio Basti, Tommaso Cremaschi
We construct an explicit quartic polynomial for which Newton's and Halley's root-finding methods both fail to converge to a root on nonempty open sets of initial values. The exampl…
Markov Chain Approximation of Sticky Diffusions and Hamilton-Jacobi-Bellman Equations on Networks
Alessio Basti, Jules Berry, Fabio Camilli
We propose a discrete Markov-chain approximation of diffusion processes on networks with both Kirchhoff and sticky vertex conditions. Stickiness is modeled by a probabilistic resid…
Kolmogorov -entropy of numerical solutions for scalar conservation laws with convex flux
Fabio Ancona, Alessio Basti, Fabio Camilli
Building on the information-theoretic perspective of P.~D.~Lax [\textit{Proc.\ Sympos., Math.\ Res.\ Center, Univ.\ Wisconsin}, 1978], we establish a two-sided quantitative compact…
A Mean Field Games Perspective on Evolutionary Clustering
Alessio Basti, Fabio Camilli, Adriano Festa
We propose a control-theoretic framework for evolutionary clustering based on quasi-stationary Mean Field Games. Each cluster is represented by a probability density whose evolutio…