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Volume 37, Issue 2
A Block Lanczos Method for the CDT Subproblem

Liqiang Song & Weihong Yang

DOI: 10.4208/jcm.1712-m2017-0064

J. Comp. Math., 37 (2019), pp. 240-260.

Published online: 2018-09

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  • Abstract

In this paper, we present a block Lanczos method for solving the large-scale CDT subproblem. During the algorithm, the original CDT subproblem is projected to a small-scale one, and then some classical methods are employed to solve this small-scale CDT subproblem to get a solution, which can be used to derive an approximate solution of the original CDT subproblem. Theoretical analysis of the error bounds for both the optimal value and the optimal solution is also proposed. Numerical experiments are carried out, and it is demonstrated that the block Lanczos method is effective and can achieve high accuracy for large-scale CDT subproblems.

  • Keywords

CDT subproblem, Trust-region subproblem, Block-Lanczos method, Krylov subspace, Error bounds.

  • AMS Subject Headings

90C20, 90C30, 65K05.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

lqsong14@fudan.edu.cn (Liqiang Song)

whyang@fudan.edu.cn (Weihong Yang)

  • BibTex
  • RIS
  • TXT
@Article{JCM-37-240, author = {Song , Liqiang and Yang , Weihong}, title = {A Block Lanczos Method for the CDT Subproblem}, journal = {Journal of Computational Mathematics}, year = {2018}, volume = {37}, number = {2}, pages = {240--260}, abstract = {

In this paper, we present a block Lanczos method for solving the large-scale CDT subproblem. During the algorithm, the original CDT subproblem is projected to a small-scale one, and then some classical methods are employed to solve this small-scale CDT subproblem to get a solution, which can be used to derive an approximate solution of the original CDT subproblem. Theoretical analysis of the error bounds for both the optimal value and the optimal solution is also proposed. Numerical experiments are carried out, and it is demonstrated that the block Lanczos method is effective and can achieve high accuracy for large-scale CDT subproblems.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1712-m2017-0064}, url = {http://global-sci.org/intro/article_detail/jcm/12678.html} }
TY - JOUR T1 - A Block Lanczos Method for the CDT Subproblem AU - Song , Liqiang AU - Yang , Weihong JO - Journal of Computational Mathematics VL - 2 SP - 240 EP - 260 PY - 2018 DA - 2018/09 SN - 37 DO - http://doi.org/10.4208/jcm.1712-m2017-0064 UR - https://global-sci.org/intro/article_detail/jcm/12678.html KW - CDT subproblem, Trust-region subproblem, Block-Lanczos method, Krylov subspace, Error bounds. AB -

In this paper, we present a block Lanczos method for solving the large-scale CDT subproblem. During the algorithm, the original CDT subproblem is projected to a small-scale one, and then some classical methods are employed to solve this small-scale CDT subproblem to get a solution, which can be used to derive an approximate solution of the original CDT subproblem. Theoretical analysis of the error bounds for both the optimal value and the optimal solution is also proposed. Numerical experiments are carried out, and it is demonstrated that the block Lanczos method is effective and can achieve high accuracy for large-scale CDT subproblems.

Song , Liqiang and Yang , Weihong. (2018). A Block Lanczos Method for the CDT Subproblem. Journal of Computational Mathematics. 37 (2). 240-260. doi:10.4208/jcm.1712-m2017-0064
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