{"paper":{"title":"An NPDo Approach for Tensor Block-Diagonalization","license":"http://creativecommons.org/licenses/by/4.0/","headline":"An NPDo method computes partial tensor block-diagonalization by maximizing the extracted block-diagonal part and converges globally while increasing the objective at each step.","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Li Wang, Mei Yang, Ren-Cang Li","submitted_at":"2026-05-13T03:09:54Z","abstract_excerpt":"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"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"It is shown the NPDo approach combined with Gauss-Seidel-type updating is globally convergent to a stationary point while the objective increases monotonically.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The premise that maximizing the extracted block-diagonal part via mode multiplications by orthonormal matrices optimally represents the tensor for the chosen block sizes.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"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.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"An NPDo method computes partial tensor block-diagonalization by maximizing the extracted block-diagonal part and converges globally while increasing the objective at each step.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"d5b5b788e514d61ffc31211009fb168bfbe1d319841fdb7e7b22fb29dbbaada3"},"source":{"id":"2605.12932","kind":"arxiv","version":1},"verdict":{"id":"d1223513-9dec-4b70-ad2d-c4bed445c3f4","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T18:58:03.214224Z","strongest_claim":"It is shown the NPDo approach combined with Gauss-Seidel-type updating is globally convergent to a stationary point while the objective increases monotonically.","one_line_summary":"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.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The premise that maximizing the extracted block-diagonal part via mode multiplications by orthonormal matrices optimally represents the tensor for the chosen block sizes.","pith_extraction_headline":"An NPDo method computes partial tensor block-diagonalization by maximizing the extracted block-diagonal part and converges globally while increasing the objective at each step."},"references":{"count":30,"sample":[{"doi":"","year":2000,"title":"Zhaojun Bai, J. 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