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Coordinatewise descent methods for leading eigenvalue problem

Publication ,  Journal Article
Yingzhou, LI; Jianfeng, LU; Wang, AZHE
Published in: SIAM Journal on Scientific Computing
January 1, 2019
Published version (DOI)

Leading eigenvalue problems for large scale matrices arise in many applications. Coordinatewise descent methods are considered in this work for such problems based on a reformulation of the leading eigenvalue problem as a nonconvex optimization problem. The convergence of several coordinatewise methods is analyzed and compared. Numerical examples of applications to quantum many-body problems demonstrate the efficiency and provide benchmarks of the proposed coordinatewise descent methods.

Duke Scholars

Jianfeng Lu
Author Jianfeng Lu Mathematics
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Published In

SIAM Journal on Scientific Computing

DOI

10.1137/18M1202505

EISSN

1095-7197

ISSN

1064-8275

Publication Date

January 1, 2019

Volume

41

Issue

4

Start / End Page

A2681 / A2716

Related Subject Headings

  • Numerical & Computational Mathematics
  • 4903 Numerical and computational mathematics
  • 4901 Applied mathematics
  • 0802 Computation Theory and Mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics
 

Citation

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Yingzhou, L. I., Jianfeng, L. U., & Wang, A. Z. H. E. (2019). Coordinatewise descent methods for leading eigenvalue problem. SIAM Journal on Scientific Computing, 41(4), A2681–A2716. https://doi.org/10.1137/18M1202505
Yingzhou, L. I., L. U. Jianfeng, and A. Z. H. E. Wang. “Coordinatewise descent methods for leading eigenvalue problem.” SIAM Journal on Scientific Computing 41, no. 4 (January 1, 2019): A2681–2716. https://doi.org/10.1137/18M1202505.
Yingzhou LI, Jianfeng LU, Wang AZHE. Coordinatewise descent methods for leading eigenvalue problem. SIAM Journal on Scientific Computing. 2019 Jan 1;41(4):A2681–716.
Yingzhou, L. I., et al. “Coordinatewise descent methods for leading eigenvalue problem.” SIAM Journal on Scientific Computing, vol. 41, no. 4, Jan. 2019, pp. A2681–716. Scopus, doi:10.1137/18M1202505.
Yingzhou LI, Jianfeng LU, Wang AZHE. Coordinatewise descent methods for leading eigenvalue problem. SIAM Journal on Scientific Computing. 2019 Jan 1;41(4):A2681–A2716.

Published In

SIAM Journal on Scientific Computing

DOI

10.1137/18M1202505

EISSN

1095-7197

ISSN

1064-8275

Publication Date

January 1, 2019

Volume

41

Issue

4

Start / End Page

A2681 / A2716

Related Subject Headings

  • Numerical & Computational Mathematics
  • 4903 Numerical and computational mathematics
  • 4901 Applied mathematics
  • 0802 Computation Theory and Mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics