On the extended direct sum conjecture
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Algebras Having Linear Multiplicative Complexities
Journal of the ACM (JACM)
Duality applied to the complexity of matrix multiplications and other bilinear forms
STOC '73 Proceedings of the fifth annual ACM symposium on Theory of computing
On the complexity of bilinear forms with commutativity
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
On the additions necessary to compute certain functions
STOC '72 Proceedings of the fourth annual ACM symposium on Theory of computing
Establishing lower bounds on algorithms: a survey
AFIPS '72 (Spring) Proceedings of the May 16-18, 1972, spring joint computer conference
Evaluating polynomials at many points
Information Processing Letters
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This paper deals with three aspects of algebraic complexity. The first section is concerned with lower bounds on the number of operations required to compute several functions. Several theorems are presented and their proofs sketched. The second section deals with relationships among the complexities of several sets of functions. In the third section, several matrices of general interest are examined and upper bounds on the number of operations required to multiply by them are constructively derived.