View in EDS

Inexact subspace projection methods for low-rank tensor eigenvalue problems.

Saved in:
Bibliographic Details
Title: Inexact subspace projection methods for low-rank tensor eigenvalue problems.
Authors: Dektor, Alec1 (AUTHOR) adektor@lbl.gov, DelMastro, Peter2 (AUTHOR), Ye, Erika1 (AUTHOR), Van Beeumen, Roel1 (AUTHOR), Yang, Chao1 (AUTHOR)
Source: Linear Algebra & its Applications. Aug2026, Vol. 743, p286-321. 36p.
Subjects: Lanczos method, Krylov subspace, Eigenvalues, Iterative methods (Mathematics)
Abstract: We propose inexact subspace iteration for solving high-dimensional eigenvalue problems with low-rank structure. Inexactness stems from low-rank compression, enabling efficient representation of high-dimensional vectors in a low-rank tensor format. A primary challenge in these methods is that standard operations, such as matrix-vector products and linear combinations, increase tensor rank, necessitating rank truncation and hence approximation. We compare the proposed methods with an existing inexact Lanczos method with low-rank compression. This method constructs an approximate orthonormal Krylov basis, which is often difficult to represent accurately in low-rank tensor formats, even when the eigenvectors themselves exhibit low-rank structure. In contrast, inexact subspace iteration uses approximate eigenvectors (Ritz vectors) directly as a subspace basis, bypassing the need for an orthonormal Krylov basis. Our analysis and numerical experiments demonstrate that inexact subspace iteration is much more robust to rank-truncation errors compared to the inexact Lanczos method. We also demonstrate that rank-truncated subspace iteration can converge for problems where the DMRG method stagnates. Furthermore, the proposed subspace iteration methods do not require a Hermitian matrix, in contrast to DMRG, which is designed specifically for Hermitian matrices. [ABSTRACT FROM AUTHOR]
Copyright of Linear Algebra & its Applications is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
FullText Text:
  Availability: 0
Header DbId: egs
DbLabel: Engineering Source
An: 193660184
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: Inexact subspace projection methods for low-rank tensor eigenvalue problems.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Dektor%2C+Alec%22">Dektor, Alec</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> adektor@lbl.gov</i><br /><searchLink fieldCode="AR" term="%22DelMastro%2C+Peter%22">DelMastro, Peter</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Ye%2C+Erika%22">Ye, Erika</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Van+Beeumen%2C+Roel%22">Van Beeumen, Roel</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Yang%2C+Chao%22">Yang, Chao</searchLink><relatesTo>1</relatesTo> (AUTHOR)
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="JN" term="%22Linear+Algebra+%26+its+Applications%22">Linear Algebra & its Applications</searchLink>. Aug2026, Vol. 743, p286-321. 36p.
– Name: Subject
  Label: Subjects
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Lanczos+method%22">Lanczos method</searchLink><br /><searchLink fieldCode="DE" term="%22Krylov+subspace%22">Krylov subspace</searchLink><br /><searchLink fieldCode="DE" term="%22Eigenvalues%22">Eigenvalues</searchLink><br /><searchLink fieldCode="DE" term="%22Iterative+methods+%28Mathematics%29%22">Iterative methods (Mathematics)</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: We propose inexact subspace iteration for solving high-dimensional eigenvalue problems with low-rank structure. Inexactness stems from low-rank compression, enabling efficient representation of high-dimensional vectors in a low-rank tensor format. A primary challenge in these methods is that standard operations, such as matrix-vector products and linear combinations, increase tensor rank, necessitating rank truncation and hence approximation. We compare the proposed methods with an existing inexact Lanczos method with low-rank compression. This method constructs an approximate orthonormal Krylov basis, which is often difficult to represent accurately in low-rank tensor formats, even when the eigenvectors themselves exhibit low-rank structure. In contrast, inexact subspace iteration uses approximate eigenvectors (Ritz vectors) directly as a subspace basis, bypassing the need for an orthonormal Krylov basis. Our analysis and numerical experiments demonstrate that inexact subspace iteration is much more robust to rank-truncation errors compared to the inexact Lanczos method. We also demonstrate that rank-truncated subspace iteration can converge for problems where the DMRG method stagnates. Furthermore, the proposed subspace iteration methods do not require a Hermitian matrix, in contrast to DMRG, which is designed specifically for Hermitian matrices. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Linear Algebra & its Applications is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=193660184
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1016/j.laa.2026.04.021
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 36
        StartPage: 286
    Subjects:
      – SubjectFull: Lanczos method
        Type: general
      – SubjectFull: Krylov subspace
        Type: general
      – SubjectFull: Eigenvalues
        Type: general
      – SubjectFull: Iterative methods (Mathematics)
        Type: general
    Titles:
      – TitleFull: Inexact subspace projection methods for low-rank tensor eigenvalue problems.
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Dektor, Alec
      – PersonEntity:
          Name:
            NameFull: DelMastro, Peter
      – PersonEntity:
          Name:
            NameFull: Ye, Erika
      – PersonEntity:
          Name:
            NameFull: Van Beeumen, Roel
      – PersonEntity:
          Name:
            NameFull: Yang, Chao
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 15
              M: 08
              Text: Aug2026
              Type: published
              Y: 2026
          Identifiers:
            – Type: issn-print
              Value: 00243795
          Numbering:
            – Type: volume
              Value: 743
          Titles:
            – TitleFull: Linear Algebra & its Applications
              Type: main
ResultId 1