Algebras Having Linear Multiplicative Complexities

descriptionPublicationkeyboard_double_arrow_right Article 01 Apr 1977 English Publisher:Association for Computing Machinery (ACM)Journal:Journal of the ACM, volume 24, pages 311-331 (issn: 0004-5411, eissn: 1557-735X,

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Authors: Charles M. Fiduccia; Yechezkel Zalcstein;

doi: 10.1145/322003.322014

Algebras Having Linear Multiplicative Complexities

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Abstract

The foundations are laid for a theory of multiplicative complexity of algebras and it is shown how “multiplication problems” such as multiplication of matrices, polynomials, quaternions, etc., are instances of this theory. The usefulness of the theory is then demonstrated by utilizing algebraic ideas and results to derive complexity bounds. In particular linear upper and lower bounds for the complexity of certain types of algebras are established.

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Keywords

Analysis of algorithms and problem complexity, Symbolic computation and algebraic computation

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