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Multi-point evaluation in higher dimensions


In this paper, we propose efficient new algorithms for multi-dimensional multi-point evaluation and interpolation on certain subsets of so called tensor product grids. These point-sets naturally occur in the design of efficient multiplication algorithms for finite-dimensional C-algebras of the form A=C[x1,...,xn]/I, where I is finitely generated by monomials of the form x1^i1 ... xn^in; one particularly important example is the algebra of truncated power series C[x1,...xn]/(x1,...,xn)^d. Similarly to what is known for multi-point evaluation and interpolation in the univariate case, our algorithms have quasi-linear time complexity. As a known consequence, we obtain fast multiplication algorithms for algebras A of the above form.
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Dates and versions

hal-00477659 , version 1 (29-04-2010)
hal-00477659 , version 2 (02-02-2012)


  • HAL Id : hal-00477659 , version 2


Joris van Der Hoeven, Eric Schost. Multi-point evaluation in higher dimensions. 2010. ⟨hal-00477659v2⟩
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