Abstract / truncated to 115 words (read the full abstract)

Matrices, as natural representation of linear mappings in finite dimension, play a crucial role in signal processing and machine learning. Multiplying a vector by a full rank matrix a priori costs of the order of the number of non-zero entries in the matrix, in terms of arithmetic operations. However, matrices exist that can be applied much faster, this property being crucial to the success of certain linear transformations, such as the Fourier transform or the wavelet transform. What is the property that allows these matrices to be applied rapidly ? Is it easy to verify ? Can weapproximate matrices with ones having this property ? Can we estimate matrices having this property ? This thesis ... toggle 8 keywords

transformée rapide – grande dimension – factorisation matricielle – traitement du signal – apprentissage automatique – données massives – factorisation d'opérateurs – optimisation mathématique

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