Abstract
In the implicitly restarted generalized second-order Arnoldi (GSOAR) method, we can get $2m$ approximate eigenpairs by projecting the quadratic eigenvalue problem (QEP) onto an $m$-dimensional subspace. During implicitly restarted processes, the problem is the mismatch between the number of shifts and the dimension of the subspace. In order to cure the problem, a new shift strategy for GSOAR method is proposed in this paper. We proof that the novel method can use all $2l$ shift candidates and preserve the special structure. Numerical experiments illustrate that the new method enhances the overall efficiency of the algorithm by increasing the efficiency of every restart process.
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