New algorithms are proposed for the Tucker approximation of a 3-tensor, thataccess it using only the tensor-by-vector-by-vector multiplication subroutine.In the matrix case, Krylov methods are methods of choice to approximate thedominant column and row subspaces of a sparse or structured matrix giventhrough the matrix-by-vector multiplication subroutine. Using the Wedderburnrank reduction formula, we propose an algorithm of matrix approximation thatcomputes Krylov subspaces and allows generalization to the tensor case. Severalvariants of proposed tensor algorithms differ by pivoting strategies, overallcost and quality of approximation. By convincing numerical experiments we showthat the proposed methods are faster and more accurate than the minimal Krylovrecursion, proposed recently by Elden and Savas.
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