Algorithms associated with arithmetic, geometric and harmonic means and integrable systems

DOI10.1016/S0377-0427(00)00316-2zbMath0982.65136MaRDI QIDQ5939867

Yoshimasa Nakamura

Publication date: 23 July 2001

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

chaotic dynamicsintegrable systemsdynamical systemarithmetic-geometric mean algorithmarithmetic-harmonic mean algorithmelliptic theta function solutioninformation geometrymax-plus limitpositive-definite matrices

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Numerical chaos (65P20) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15)

Related Items (5)

Partial-skew-orthogonal polynomials and related integrable lattices with Pfaffian tau-functions ⋮ Quasi-arithmetic centers, quasi-arithmetic mixtures, and the Jensen-Shannon \(\nabla \)-divergences ⋮ An extended multistep Shanks transformation and convergence acceleration algorithm with their convergence and stability analysis ⋮ Maps on statistical manifolds exactly reduced from the Perron-Frobenius equations for solvable chaotic maps ⋮ Determinantal solutions of solvable chaotic systems

Cites Work

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• Completely integrable gradient systems on the manifolds of Gaussian and multinomial distributions
• Operator means and matrix functions
• The QR algorithm and scattering for the finite nonperiodic Toda lattice
• Aitken-Steffensen acceleration and a new addition formula for Fibonacci numbers
• Theory of nonlinear lattices
• The matrix sign function and computations in systems
• On an integrable discretization of the Rayleigh quotient gradient system and the power method with a shift
• Continuous versions of some discrete maps or what goes on when the lights go out
• Differential-geometrical methods in statistics
• Dualistic differential geometry of positive definite matrices and its applications to related problems
• Dynamical systems that sort lists, diagonalize matrices, and solve linear programming problems
• FAST COMPUTATION OF MATRIX EXPONENTIAL AND LOGARITHM
• Matrix Analysis
• Calculating Laplace Transforms in Terms of the Toda Molecule
• Ultradiscrete KdV Equation

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