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SUMMARYIn this paper, an eigenvalue problem that involves uncertain-but-non-random parameters is discussed. A new method is developed to evaluate the reliable upper and lower bounds on frequencies of structures for these problems. In this method the matrix in the deviation amplitude interval is considered to be a perturbation around the nominal value of the interval matrix, and the upper and lower bounds to the maximum and minimum eigenvalues of this perturbation matrix are computed, respectively. Then based on the matrix perturbation theory, the eigenvalue bounds of the original interval eigenvalue problem can be obtained. Finally, two numerical examples are provided and the results show that the proposed method is reliable and efficient.

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SUMMARYIn this study, a new method with algorithms for computing bounds to real eigenvalues of real-interval matrices is developed. The algorithms are based on the properties of continuous functions. The method can provide the tightest eigenvalue bounds and improve some former research results. Numerical examples illustrate the applicability and effectiveness of the new method.