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 -algebras of the form ,...
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| Vydáno v: | Applicable algebra in engineering, communication and computing Ročník 24; číslo 1; s. 37 - 52 |
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| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Berlin/Heidelberg
Springer-Verlag
01.01.2013
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| Témata: | |
| ISSN: | 0938-1279, 1432-0622 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | 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
-algebras of the form
, where
is generated by monomials of the form
; one particularly important example is the algebra of truncated power series
. 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 Schost (ISSAC’05, ACM, New York, NY, pp 293–300,
2005
), we obtain fast multiplication algorithms for algebras
of the above form. |
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| ISSN: | 0938-1279 1432-0622 |
| DOI: | 10.1007/s00200-012-0179-3 |