A Block Lanczos Method for the CDT Subproblem (Journal of Computational Mathematics, 2018)
In this paper, we present a block Lanczos method for solving the large-scale CDTsubproblem. During the algorithm, the original CDT subproblem is projected to a small-scaleone, and then some classical methods are employed to solve this small-scale CDTsubproblem to get a solution, which can be used to derive an approximate solution of theoriginal CDT subproblem. Theoretical analysis of the error bounds for both the optimalvalue 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 highaccuracy for large-scale CDT subproblems.
Keywords: CDT subproblem; Trust-region subproblem; Block-Lanczos method; Krylov subspace; Error bounds.