The ultradiscrete Toda lattice and the Smith normal form of bidiagonal matrices

DOI10.1063/5.0056498zbMath1497.37077arXiv2012.13068OpenAlexW3114713235MaRDI QIDQ5154273

Katsuki Kobayashi, Satoshi Tsujimoto

Publication date: 4 October 2021

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2012.13068

zbMATH Keywords

tridiagonal matricesSmith normal formdiscrete Toda lattice

Mathematics Subject Classification ID

Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures (37K30) Canonical forms, reductions, classification (15A21) Lattice dynamics; integrable lattice equations (37K60) Relations of finite-dimensional Hamiltonian and Lagrangian systems with Lie algebras and other algebraic structures (37J37) Completely integrable discrete dynamical systems (37J70)

Cites Work

• On efficient sparse integer matrix Smith normal form computations
• Smith normal form in combinatorics
• Accurate computation of singular values in terms of shifted integrable schemes
• Integrable discrete hungry systems and their related matrix eigenvalues
• Integrable lattices and convergence acceleration algorithms
• The discrete Lotka-Volterra system computes singular values
• Elementary Toda orbits and integrable lattices
• Polynomial Algorithms for Computing the Smith and Hermite Normal Forms of an Integer Matrix
• Proof of solitonical nature of box and ball systems by means of inverse ultra-discretization
• The discrete relativistic Toda molecule equation and a Padé approximation algorithm
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