Volume 3, Issue 1
Top Eigenpairs of Large Scale Matrices

Mu-Fa Chen & Rong-Rong Chen

CSIAM Trans. Appl. Math., 3 (2022), pp. 1-25.

Published online: 2022-03

Export citation
  • Abstract

This paper is devoted to the study of an extended global algorithm on computing the top eigenpairs of a large class of matrices. Three versions of the algorithm are presented that includes a preliminary version for real matrices, one for complex matrices, and one for large scale sparse real matrix. Some examples are illustrated as powerful applications of the algorithms. The main contributions of the paper are two localized estimation techniques, plus the use of a machine learning inspired approach in terms of a modified power iteration. Based on these new tools, the proposed algorithm successfully employs the inverse iteration with varying shifts (a very fast “cubic algorithm”) to achieve a superior estimation accuracy and computation efficiency to existing approaches under the general setup considered in this work.

  • Keywords

Matrix eigenpair, extended global algorithm, localized estimation technique, top eigenpair, large sparse matrix.

  • AMS Subject Headings

15A18, 65F15

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{CSIAM-AM-3-1, author = {Mu-Fa and Chen and and 22455 and and Mu-Fa Chen and Rong-Rong and Chen and and 22456 and and Rong-Rong Chen}, title = {Top Eigenpairs of Large Scale Matrices}, journal = {CSIAM Transactions on Applied Mathematics}, year = {2022}, volume = {3}, number = {1}, pages = {1--25}, abstract = {

This paper is devoted to the study of an extended global algorithm on computing the top eigenpairs of a large class of matrices. Three versions of the algorithm are presented that includes a preliminary version for real matrices, one for complex matrices, and one for large scale sparse real matrix. Some examples are illustrated as powerful applications of the algorithms. The main contributions of the paper are two localized estimation techniques, plus the use of a machine learning inspired approach in terms of a modified power iteration. Based on these new tools, the proposed algorithm successfully employs the inverse iteration with varying shifts (a very fast “cubic algorithm”) to achieve a superior estimation accuracy and computation efficiency to existing approaches under the general setup considered in this work.

}, issn = {2708-0579}, doi = {https://doi.org/10.4208/csiam-am.2021-0005}, url = {http://global-sci.org/intro/article_detail/csiam-am/20286.html} }
TY - JOUR T1 - Top Eigenpairs of Large Scale Matrices AU - Chen , Mu-Fa AU - Chen , Rong-Rong JO - CSIAM Transactions on Applied Mathematics VL - 1 SP - 1 EP - 25 PY - 2022 DA - 2022/03 SN - 3 DO - http://doi.org/10.4208/csiam-am.2021-0005 UR - https://global-sci.org/intro/article_detail/csiam-am/20286.html KW - Matrix eigenpair, extended global algorithm, localized estimation technique, top eigenpair, large sparse matrix. AB -

This paper is devoted to the study of an extended global algorithm on computing the top eigenpairs of a large class of matrices. Three versions of the algorithm are presented that includes a preliminary version for real matrices, one for complex matrices, and one for large scale sparse real matrix. Some examples are illustrated as powerful applications of the algorithms. The main contributions of the paper are two localized estimation techniques, plus the use of a machine learning inspired approach in terms of a modified power iteration. Based on these new tools, the proposed algorithm successfully employs the inverse iteration with varying shifts (a very fast “cubic algorithm”) to achieve a superior estimation accuracy and computation efficiency to existing approaches under the general setup considered in this work.

Mu-Fa Chen & Rong-Rong Chen. (2022). Top Eigenpairs of Large Scale Matrices. CSIAM Transactions on Applied Mathematics. 3 (1). 1-25. doi:10.4208/csiam-am.2021-0005
Copy to clipboard
The citation has been copied to your clipboard