An NPDo approach is developed for computing Principal Tensor Block-Diagonalization of tensors, generalizing Tucker decomposition and approximate tensor SVD, with a Gauss-Seidel update shown to be globally convergent to a stationary point.
An NPDo Approach for Principal Joint SVD-type Block Diagonalization
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abstract
This paper is concerned with partial Joint SVD-type Block Diagonalization of several matrices so that the extracted diagonal parts collectively optimally assume part of the total mass of all given matrices. For that reason, it will be referred also as Principal Joint SVD-type Block Diagonalization. When each block-size is 1-by-1, it is about finding a dominant partial joint SVD decomposition for the matrices of interests. An NPDo approach is proposed for maximizing the common dominant block-diagonal parts collectively. It is shown that the NPDo approach combined with Gauss-Seidel-type updating is globally convergent to a stationary point while the objective increases monotonically. Numerical experiments are presented to illustrate the efficiency of the NPDo approach.
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An NPDo Approach for Tensor Block-Diagonalization
An NPDo approach is developed for computing Principal Tensor Block-Diagonalization of tensors, generalizing Tucker decomposition and approximate tensor SVD, with a Gauss-Seidel update shown to be globally convergent to a stationary point.