Abstract
New algorithms are proposed for the Tucker approximation of a 3-tensor accessed only through a tensor-by-vector-by-vector multiplication subroutine. In the matrix case, the Krylov methods are methods of choice to approximate the dominant column and row subspaces of a sparse or structured matrix given through a matrix-by-vector operation. Using the Wedderburn rank reduction formula, we propose a matrix approximation algorithm that computes the Krylov subspaces and can be generalized to 3-tensors. The numerical experiments show that on quantum chemistry data the proposed tensor methods outperform the minimal Krylov recursion of Savas and Eldén.
Original language | English |
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Journal | SIAM Journal on Scientific Computing |
Volume | 34 |
Issue number | 1 |
DOIs | |
Publication status | Published - 28 May 2012 |
Keywords
- Fast compression
- Krylov subspace methods
- Multidimensional arrays
- Sparse tensors
- Structured tensors
- Tucker approximation
- Wedderburn rank reduction