Tractability of tensor product problems in the average case setting

It has been an open problem to derive a necessary and sufficient condition for a linear tensor product problem S = {Sd} in the average case setting to be weakly tractable but not polynomially tractable. As a result of the tensor product structure, the eigenvalues of the covariance operator of the induced measure in the one dimensional problem characterize the complexity of approximating Sd, d ≥ 1, with accuracy ε. If ∞ j=1 λj < 1 and λ2 > 0, we know that S is not polynomially tractable

• Type: Journal
• Year: 2011
• Where: JC
• Authors: Anargyros Papageorgiou, Iasonas Petras
• Keywords: JC 2011, Tensor Product, Tensor Product Problem, Tensor Product Structure