´ ` DIRIGER DES RECHERCHES MEMOIRE D’HABILITATION A pr´esent´e le 30 mars 2018

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• Operations research
• Parallel computing
• Mathematics
• Planning
• Scheduling
• Mathematical optimization
• Algorithm
• Applied mathematics
• Graph partition

Proposal for a Standardization of Mathematical Function Implementation in Floating-Point Arithmetic David Defour Guillaume Hanrot Jean-Michel Muller

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• Computer arithmetic
• Arithmetic
• Mathematics
• Computer architecture
• Rounding
• IEEE 754
• Double-precision floating-point format
• Interval arithmetic
• Significant figures
• NaN
• Sine
• Signed zero

Introduction Taylor model arithmetic using floating-point arithmetic Getting even more accuracy Conclusion Diddl - Goletz

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• Computer arithmetic
• cole normale suprieure de Lyon
• Floating-point arithmetic

Computing minimal interpolation bases

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• Algebra
• Mathematics
• Interpolation
• Polynomial interpolation
• Polynomials
• Permutation
• Jordan normal form
• Pad approximant
• Random self-reducibility
• Pattern language

LLL reducing with the most significant bits Saruchi Ivan Morel Indian Institute of Technology New Delhi

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comput. complex), 91 – 030091–40 DOIs00037c Birkh¨

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• Algebra
• Mathematics
• Linear algebra
• Matrix theory
• Determinant
• Frobenius normal form
• Matrix
• Characteristic polynomial
• Polynomial matrix
• Euclidean algorithm
• Matrix exponential
• Invertible matrix

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