Fast change of basis in algebras | Zendy

Irvin Roy Hentzel | Zendy; David P. Jacobs | Zendy

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Fast change of basis in algebras

Author(s) -

Irvin Roy Hentzel,

David P. Jacobs

Publication year - 1992

Publication title -

applicable algebra in engineering communication and computing

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.558

H-Index - 35

eISSN - 1432-0622

pISSN - 0938-1279

DOI - 10.1007/bf01294835

Subject(s) - multiplication (music) , basis (linear algebra) , transformation (genetics) , matrix multiplication , mathematics , matrix (chemical analysis) , transformation matrix , constant (computer programming) , arithmetic , algorithm , algebra over a field , combinatorics , pure mathematics , computer science , geometry , physics , biochemistry , chemistry , materials science , kinematics , classical mechanics , quantum mechanics , composite material , quantum , gene , programming language

Given ann-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(n?) matrix multiplication algorithm, we show how to solve the problem in time O(n?+1). Using the method of Coppersmith and Winograd, this yields an algorithm ofO(n3.376).

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