Fast change of basis in algebras

Date
1992-12-01
Authors
Hentzel, Irvin
Hentzel, Irvin
Jacobs, David
Major Professor
Advisor
Committee Member
Journal Title
Journal ISSN
Volume Title
Publisher
Altmetrics
Authors
Research Projects
Organizational Units
Mathematics
Organizational Unit
Journal Issue
Series
Department
Mathematics
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).

Comments

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.

Description
Keywords
Citation
DOI
Collections