Convergence of a Jacobi-type method for the approximate orthogonal tensor diagonalization (CROSBI ID 316539)
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Begović Kovač, Erna
engleski
Convergence of a Jacobi-type method for the approximate orthogonal tensor diagonalization
For a general third-order tensor the paper studies two closely related problems, an SVD-like tensor decomposition and an (approximate) tensor diagonalization. We develop a Jacobi-type algorithm that works on 2x2x2 subtensors and, in each iteration, maximizes the sum of squares of its diagonal entries. We show how the rotation angles are calculated and prove convergence of the algorithm. Different initializations of the algorithm are discussed, as well as the special cases of symmetric and antisymmetric tensors. The algorithm can be generalized to work on higher-order tensors.
Jacobi-type methods; convergence; tensor diagonalization; tensor decompositions; SVD
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