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Ehemalige Mitarbeiter

Prof. Dr. Martin Lotz

Lupe

Kontakt
Mathematics Institute
Zeeman Building
University of Warwick
Coventry CV4 7AL
United Kingdom
 
Persönliche Homepage
http://homepages.warwick.ac.uk/staff/Martin.Lotz/

Publikationen in der Arbeitsgruppe

Lower Bounds on the Bounded Coefficient Complexity of Bilinear Maps
Citation key BL-Lower-Bounds-On-The-Bounded-Coefficient-Complexity-Of-Bilinear-Maps
Author Peter Bürgisser and Martin Lotz
Pages 464-482
Year 2004
Journal Journal of the ACM
Volume 51
Number 3
Abstract We prove lower bounds of order $nłog n$ for both the problem of multiplying polynomials of degree $n$, and of dividing polynomials with remainder, in the model of bounded coefficient arithmetic circuits over the complex numbers. These lower bounds are optimal up to order of magnitude. The proof uses a recent idea of R. Raz [Proc.\ 34th STOC 2002] proposed for matrix multiplication. It reduces the linear problem of multiplying a random circulant matrix with a vector to the bilinear problem of cyclic convolution. We treat the arising linear problem by extending J. Morgenstern's bound [J.\ ACM 20, pp.\ 305-306, 1973] in a unitarily invariant way. This establishes a new lower bound on the bounded coefficient complexity of linear forms in terms of the singular values of the corresponding matrix. In addition, we extend these lower bounds for linear and bilinear maps to a model of circuits that allows a restricted number of unbounded scalar multiplications.
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