Refined bounds on the convergence of block Lanczos method for extended trust-region subproblem

Extended trust-region (ETR) subproblem plays an important role in many applications. The block Lanczos method proposed in Song and Yang, (2019) [27] is an efficient approach for solving large-scale ETR subproblem. In this method, the large-scale ETR subproblem is projected into a small-sized ETR subproblem by using the block Lanczos process, and some error bounds are established. However, the error bounds on the optimal value, the optimal solution, and the multipliers are not sharp enough. In this paper, we revisit the convergence of the block Lanczos method and refine all the error bounds. Examples are given to show the superiority of our theoretical results over the existing ones. (c) 2022 IMACS. Published by Elsevier B.V. All rights reserved.