Abstract
It has been an open problem to derive a necessary and sufficient condition for a linear tensor product problem to be weakly tractable in the worst case. The complexity of linear tensor product problems in the worst case depends on the eigenvalues { λ i } i ∈ N of a certain operator. It is known that if λ 1 = 1 and λ 2 ∈ ( 0 , 1 ) then λ n = o ( ( ln n ) − 2 ) , as n → ∞ , is a necessary condition for a problem to be weakly tractable. We show that this is a sufficient condition as well.
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