Article
Fast change of basis in algebras
Applicable Algebra in Engineering, Communication and Computing
Document Type
Article
Disciplines
- Algebra and
- Mathematics
Publication Version
Accepted Manuscript
Publication Date
12-1-1992
DOI
10.1007/BF01294835
Abstract
Given an n-dimensional algebraA represented by a basisB and structure constants, and given a transformation matrix for a new basisC., we wish to compute the structure constants forA relative to C. There is a straightforward way to solve this problem inO(n5) arithmetic operations. However given an O(nω) matrix multiplication algorithm, we show how to solve the problem in time O(nω+1). Using the method of Coppersmith and Winograd, this yields an algorithm ofO(n3.376).
Copyright Owner
Springer-Verlag
Copyright Date
1992
Language
en
File Format
application/pdf
Citation Information
Irvin R. Hentzel and David Pokrass Jacobs. "Fast change of basis in algebras" Applicable Algebra in Engineering, Communication and Computing Vol. 3 Iss. 4 (1992) p. 257 - 261 Available at: http://works.bepress.com/irvin-hentzel/11/
The final publication is available at Springer via https://doi.org/10.1007/BF01294835. Hentzel, Irvin Roy, and David Pokrass Jacobs. "Fast change of basis in algebras." Applicable Algebra in Engineering, Communication and Computing 3, no. 4 (1992): 257-261. doi:10.1007/BF01294835. Posted with permission.