An NPDo Approach for Tensor Block-Diagonalization
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914562541879296 |
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| author | Li, Ren-Cang Wang, Li Yang, Mei |
| author_facet | Li, Ren-Cang Wang, Li Yang, Mei |
| contents | This paper is concerned with Partial Tensor Block-Diagonalization of a multiway tensor by orthonormal matrices so that the extracted block-diagonal part optimally represents the tensor. The basic idea is to maximize the block-diagonal part via the tensor's mode-multiplications by orthonormal matrices. For that reason, it will be referred to Principal Tensor Block-Diagonalization (PTBD), which contains the Tucker decomposition (TD) of a tensor as a special case with just one block. Also as a special case is the approximate dominant tensor SVD in which each block-size is 1-by-1. An NPDo approach is proposed to optimize the block-diagonal part for computing \ptbd. It is shown 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_12932 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An NPDo Approach for Tensor Block-Diagonalization Li, Ren-Cang Wang, Li Yang, Mei Numerical Analysis 15A18, 15A69, 65F30, 65K05, 90C26 This paper is concerned with Partial Tensor Block-Diagonalization of a multiway tensor by orthonormal matrices so that the extracted block-diagonal part optimally represents the tensor. The basic idea is to maximize the block-diagonal part via the tensor's mode-multiplications by orthonormal matrices. For that reason, it will be referred to Principal Tensor Block-Diagonalization (PTBD), which contains the Tucker decomposition (TD) of a tensor as a special case with just one block. Also as a special case is the approximate dominant tensor SVD in which each block-size is 1-by-1. An NPDo approach is proposed to optimize the block-diagonal part for computing \ptbd. It is shown 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. |
| title | An NPDo Approach for Tensor Block-Diagonalization |
| topic | Numerical Analysis 15A18, 15A69, 65F30, 65K05, 90C26 |
| url | https://arxiv.org/abs/2605.12932 |