Foreword / Avant-propos

Avant Propos

Avant-propos.

Kantorovitch's theorem gives su cient conditions for the convergence of Newton's method. We presenta full formalization of this theorem in the case of a real function. The work is accomplished inside the Coqproof assistant and it is based on the Reals library provided by the theorem prover. For the general case ofthe theorem we rst describe a way to represent concepts from multivari...

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o think that the neoimpressionists are painters who cover canvases with little multicolored spots is a rather widespread mistake, " wrote Paul Signac in his manifesto of their movement. " This mediocre dot method has nothing to do with the aesthetic of the painters we are defending here, nor with the technique of divisionism they use. " Signac was referring to, among others, Georges Seurat, who...

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