On the tractability of linear tensor product problems in the worst case

  • Authors:

  • Anargyros Papageorgiou;Iasonas Petras

  • Affiliations:

  • Department of Computer Science, Columbia University, New York, NY 10027, United States;Department of Computer Science, Columbia University, New York, NY 10027, United States

  • Venue:
  • Journal of Complexity
  • Year:
  • 2009

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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 {@l"i}"i"@?"N of a certain operator. It is known that if @l"1=1 and @l"2@?(0,1) then @l"n=o((lnn)^-^2), as n-~, is a necessary condition for a problem to be weakly tractable. We show that this is a sufficient condition as well.