Abstract：
The memory-efficient Two-level Orthogonal Arnoldi method can maintain the similar numerical stability and convergence to the standard Arnoldi method, therefore it becomes an important method to solve quadratic eigenvalue problems. It is inevitable to restart the algorithm in practical applications since the computation and storage continue to increase during the process. The special structure of decomposition puts forward new requirements for the restarted algorithm. In this paper, we analyse the properties of the restarted subspace and propose a restarted method which maintains the special structure. On the basis of that, we use Schur decomposition, exact shifts and refined shifts within the restarted method to obtain three restarted algorithms. Theoretical analysis and numerical results illustrate the efficiency of the restarted algorithms under fixed maximum storage.
. IMPLICITLY RESTARTED TWO-LEVEL ORTHOGONAL ARNOLDI ALGORITHMS[J]. Journal of Numerical Methods and Computer Applicat, 2017, 38(4): 256-270.
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