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On the Validity of the Direct Sum Conjecture

SIAM Journal on Computing, 1986
The direct sum conjecture states that the multiplicative complexity of disjoint sets of bilinear computations is the sum of their separate multiplicative complexities. This conjecture is known to hold for only a few specialized cases. In this paper, we establish its validity for large classes of computations.
Joseph F. JáJá, Jean Takche
openaire   +5 more sources

Sum and direct sum of frame sequences

Linear and Multilinear Algebra, 2013
Casazza, Han and Larson characterized various properties of the direct sum of two frame sequences. We add characterizations of other properties and study the relationship between the direct sum and the sum of frame sequences. In particular, we find a necessary and sufficient condition for the sum of two strongly disjoint (orthogonal) frame sequences ...
Yoo Young Koo, Jae Kun Lim
openaire   +3 more sources

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