A convergent hierarchy of non-linear eigenproblems to compute the joint spectral radius of nonnegative matrices

DOI10.3934/mcrf.2020011zbMath1476.65080arXiv1805.03284OpenAlexW2996476674WikidataQ126412059 ScholiaQ126412059MaRDI QIDQ827557

Stéphane Gaubert, Nikolas Stott

Publication date: 13 January 2021

Published in: Mathematical Control and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1805.03284

zbMATH Keywords

iterative methodnonnegative matricesjoint spectral radiusrisk sensitive controlKrasnoselskii-Mann iterationnonlinear eigenproblementropy gamesPerron-Frobenius method

Mathematics Subject Classification ID

Dynamic programming in optimal control and differential games (49L20) Numerical solution of nonlinear eigenvalue and eigenvector problems (65H17) Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) (93C30)

Related Items (6)

The Tropical Nullstellensatz and Positivstellensatz for Sparse Polynomial Systems ⋮ Tropical Linear Regression and Mean Payoff Games: Or, How to Measure the Distance to Equilibria ⋮ A unified approach to nonlinear Perron-Frobenius theory ⋮ Convergence of iterates in nonlinear Perron-Frobenius theory ⋮ Spectral inequalities for nonnegative tensors and their tropical analogues ⋮ The operator approach to entropy games

Cites Work

• Unnamed Item
• Spectral simplex method
• Stability of discrete-time switching systems with constrained switching sequences
• Anti-dissipative schemes for advection and application to Hamilton-Jacobi-bellmann equations
• Iterative building of Barabanov norms and computation of the joint spectral radius for matrix sets
• On a discrete approximation of the Hamilton-Jacobi equation of dynamic programming
• Convexity and log convexity for the spectral radius
• Lyapunov indicator of discrete inclusions. I
• Discrete time high-order schemes for viscosity solutions of Hamilton- Jacobi-Bellman equations
• Eigenvalues for a class of homogeneous cone maps arising from max-plus operators
• An efficient algorithm for Hamilton-Jacobi equations in high dimension
• Perron-Frobenius theorem for nonnegative multilinear forms and extensions
• Exact computation of joint spectral characteristics of linear operators
• On the rate of convergence of Krasnosel'skiĭ-Mann iterations and their connection with sums of Bernoullis
• Hilbert's metric and positive contraction mappings in a Banach space
• The operator approach to entropy games
• Generic uniqueness of the bias vector of finite zero-sum stochastic games with perfect information
• Uniqueness of the fixed point of nonexpansive semidifferentiable maps
• TROPICAL POLYHEDRA ARE EQUIVALENT TO MEAN PAYOFF GAMES
• Convergence Rate for a Curse-of-Dimensionality-Free Method for a Class of HJB PDEs
• Weak Finsler structures and the Funk weak metric
• Two approximations of solutions of Hamilton-Jacobi equations
• A maximin characterisation of the escape rate of non-expansive mappings in metrically convex spaces
• A Curse-of-Dimensionality-Free Numerical Method for Solution of Certain HJB PDEs
• Polynomial-Time Computation of the Joint Spectral Radius for Some Sets of Nonnegative Matrices
• Hilbert’s projective metric and iterated nonlinear maps
• Nonexpansive Mappings, Asymptotic Regularity and Successive Approximations
• Fixed Points and Iteration of a Nonexpansive Mapping in a Banach Space
• Entropy Games and Matrix Multiplication Games
• The Perron-Frobenius theorem for homogeneous, monotone functions
• Contraction of Riccati Flows Applied to the Convergence Analysis of a Max-Plus Curse-of-Dimensionality--Free Method
• Stability of Linear Problems: Joint Spectral Radius of Sets of Matrices
• Joint Spectral Radius and Path-Complete Graph Lyapunov Functions
• A Variational Formula for Risk-Sensitive Reward
• Mean Value Methods in Iteration

This page was built for publication: A convergent hierarchy of non-linear eigenproblems to compute the joint spectral radius of nonnegative matrices