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An inverse eigenvalue problem and a matrix approximation problem for symmetric skew-hamiltonian matrices

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Abstract

Based on the theory of inverse eigenvalue problem, a correction of an approximate model is discussed, which can be formulated as NX=XΛ, 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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Authors and Affiliations

  1. Department of Mathemathics, Institute of Machinery Industry, Beijing, 100085, China

    Dongxiu Xie, Ningjun Huang & Qin Zhang

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  1. Dongxiu Xie
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  2. Ningjun Huang
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  3. Qin Zhang
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Correspondence to Dongxiu Xie.

Additional information

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

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