A smoothing Newton's method for the construction of a damped vibrating system from noisy test eigendata |
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Authors: | Zheng‐Jian Bai Wai‐Ki Ching |
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Affiliation: | 1. Department of Information and Computational Mathematics, Xiamen University, Xiamen 361005, People's Republic of China;2. Advanced Modeling and Applied Computing Laboratory, Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong |
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Abstract: | In this paper we consider an inverse problem for a damped vibration system from the noisy measured eigendata, where the mass, damping, and stiffness matrices are all symmetric positive‐definite matrices with the mass matrix being diagonal and the damping and stiffness matrices being tridiagonal. To take into consideration the noise in the data, the problem is formulated as a convex optimization problem involving quadratic constraints on the unknown mass, damping, and stiffness parameters. Then we propose a smoothing Newton‐type algorithm for the optimization problem, which improves a pre‐existing estimate of a solution to the inverse problem. We show that the proposed method converges both globally and quadratically. Numerical examples are also given to demonstrate the efficiency of our method. Copyright © 2008 John Wiley & Sons, Ltd. |
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Keywords: | damped vibrating system eigendata quadratic eigenvalue problem inverse quadratic eigenvalue problem Newton's method |
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