Abstract
This paper concerns the eigenvalue embedding problem (EEP) of updating a symmetric finite-element model so that a few troublesome eigenvalues are replaced by some chosen ones, while the remaining large number of eigenvalues and eigenvectors of the original model do not change. Based on the theory established in [2], by sufficiently utilizing the inherent freedom of the EEP, an expression of the parameterized solution to the EEP is derived. This expression is then used to develop a novel numerical method for solving the EEP, in which the parameters in the solutions are optimized in some sense. This method not only utilizes the freedom of the EEP but also removes the limitation of the method proposed in [6]. The results of our numerical experiments show that the present algorithm is feasible and efficient, and can outperform the iterative method in [3] and the method in [6].
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