## Abstract

Based on the theory of inverse eigenvalue problem, a correction of an approximate model is discussed, which can be formulated as *NX*=*X*Λ, where *X* and Λ are given identified modal and eigenvalues matrices, respectively. The solvability conditions for a symmetric skew-Hamiltonian matrix *N* are established and an explicit expression of the solutions is derived. For any estimated matrix *C* of the analytical model, the best approximation matrix \(\widehat{N}\) to minimize the Frobenius norm of *C* − *N* is provided and some numerical results are presented. A perturbation analysis of the solution \(\widehat{N}\) is also performed, which has scarcely appeared in existing literatures.

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Supported by the National Natural Science Foundation of China(10571012, 10771022), the Beijing Natural Science Foundation (1062005) and the Beijing Educational Committee Foundation (KM200411232006, KM200611232010).

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Xie, D., Huang, N. & Zhang, Q. An inverse eigenvalue problem and a matrix approximation problem for symmetric skew-hamiltonian matrices.
*Numer Algor* **46**, 23–34 (2007). https://doi.org/10.1007/s11075-007-9124-0

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DOI: https://doi.org/10.1007/s11075-007-9124-0