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Contributions to the Formal Verification of Arithmetic Algorithms
The Floating-Point (FP) implementation of a real-valued function is performed with correct rounding if the output is always equal to the rounding of the exact value,... -
A non-linear set-membership approach for the control of Discrete Event Systems
International audience -
Interval analysis and robotics
International audience -
Relaxed method to certify the solution of a linear system
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Tradeoffs between Accuracy and Efficiency for Interval Matrix Multiplication
International audience -
Interval matrix multiplication on parallel architectures
International audience -
Efficient algorithms for verified scientific computing : Numerical linear alg...
Interval arithmetic is a means to compute verified results. However, a naive use of interval arithmetic does not provide accurate enclosures of the exact results.... -
A library of Taylor models for PVS automatic proof checker
We present in this report a library to compute with Taylor models, a technique extending interval arithmetic to reduce decorrelation and to solve differential... -
Tradeoffs between Accuracy and Efficiency for Optimized and Parallel Interval...
International audience -
N-ary algebras. Arithmetic of intervals
This thesis has two distinguish parts. The first part concerns the study of n-ary algebras. A n-ary algebra is a vector space with a multiplication on n arguments.... -
Particle Swarm Optimization for solving engineering problems: a new constrain...
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A Generic Lazy Evaluation Scheme for Exact Geometric Computations
We present a generic C++ design to perform efficient and exact geometric computations using lazy evaluations. Exact geometric computations are critical for the... -
A proposal for the C++ standard : Bool_set, multi-valued logic
We propose a design for multi-valued logic, for integration into the C++ standard. The main motivation for this class comes from interval arithmetic, where it can be... -
Parallel Implementation of Interval Matrix Multiplication
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Numerical Reproducibility and Parallel Computations: Issues for Interval Algo...
International audience -
Numerical reproducibility in HPC: the interval point of view
International audience -
Reliable Outer Bounds for the Dual Simplex Algorithm with Interval Right-hand...
International audience -
Latest Developments on the IEEE 1788 Effort for the Standardization of Interv...
(Standardization effort supported by the INRIA D2T.)
