Taylor models and floating-point arithmetic: proof that arithmetic operations are validated in COSY

DOI10.1016/j.jlap.2004.07.008zbMath1080.68519OpenAlexW2009101896MaRDI QIDQ1779571

Nathalie Revol, Martin Berz, Kyoko Makino

Publication date: 1 June 2005

Published in: The Journal of Logic and Algebraic Programming (Search for Journal in Brave)

Full work available at URL: https://hal.inria.fr/inria-00071850/file/RR-4737.pdf

zbMATH Keywords

Taylor modelContainment propertyCOSY softwareFloating-point operationRounding errorValidated result

Mathematics Subject Classification ID

Mathematical problems of computer architecture (68M07)

Related Items (18)

A study of rigorous ODE integrators for multi-scale set-oriented computations ⋮ An application of Taylor models to the Nakao method on ODEs ⋮ Validated Modeling of Mechanical Systems with SmartMOBILE: Improvement of Performance by ValEncIA-IVP ⋮ Dynamics of spatial rigid-flexible multibody systems with uncertain interval parameters ⋮ Validated solutions of initial value problems for parametric ODEs ⋮ Computing Reachable Sets of Differential Inclusions ⋮ Lie symmetries applied to interval integration ⋮ An efficient approach to solve very large dense linear systems with verified computing on clusters ⋮ Rigorous and accurate enclosure of invariant manifolds on surfaces ⋮ Interval uncertain method for multibody mechanical systems using Chebyshev inclusion functions ⋮ Solving set-valued constraint satisfaction problems ⋮ A polynomial chaos expansion approach for nonlinear dynamic systems with interval uncertainty ⋮ A validated real function calculus ⋮ Quantum computing as a particular case of computing with tensors ⋮ Rigorous Estimation of Floating-Point Round-off Errors with Symbolic Taylor Expansions ⋮ A new hybrid uncertainty optimization method for structures using orthogonal series expansion ⋮ Computing Capture Tubes ⋮ Non-intrusive hybrid interval method for uncertain nonlinear systems using derivative information

Uses Software

• mctoolbox
• Cosy

Cites Work

• Unnamed Item
• Verified integration of ODEs and flows using differential algebraic methods on high-order Taylor models
• New methods for high-dimensional verified quadrature
• Adaptive precision floating-point arithmetic and fast robust geometric predicates
• Verification of invertibility of complicated functions over large domains
• Higher order verified inclusions of multidimensional systems by Taylor models.
• A floating-point technique for extending the available precision
• Interval Methods for Systems of Equations
• Accuracy and Stability of Numerical Algorithms
• Verified high-order inversion of functional dependencies and interval Newton methods

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