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

Abstract

Based on the theory of inverse eigenvalue problem, a correction of an approximate model is discussed, which can be formulated as N X = X , where X and 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 matrixN to minimize the Frobenius norm of C − N is provided and some numerical results are presented. A perturbation analysis of the solutionN is also performed, which has scarcely appeared in existing literatures.

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