Abstract
Identification of the Volterra system is an ill-posed problem. We propose a regularization method for solving this ill-posed problem via a multiscale collocation method with multiple regularization parameters corresponding to the multiple scales. Many highly nonlinear problems such as flight data analysis demand identifying the system of a high order. This task requires huge computational costs due to processing a dense matrix of a large order. To overcome this difficulty a compression strategy is introduced to approximate the full matrix resulted in collocation of the Volterra kernel by an appropriate sparse matrix. A numerical quadrature strategy is designed to efficiently compute the entries of the compressed matrix. Finally, numerical results of three simulation experiments are presented to demonstrate the accuracy and efficiency of the proposed method.
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Communicated by Juan Manuel Peña.
Supported in part by the US National Aeronautics and Space Administration under Cooperative Agreement NNX07AC37A, by the US National Science Foundation under grants CCR-0407476 and DMS-0712827, by the Natural Science Foundation of China under grants 10371122 and 10631080, and by the Education Ministry of the People’s Republic of China under the Changjiang Scholar Chair Professorship Program through Sun Yat-sen University.
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Brenner, M., Jiang, Y. & Xu, Y. Multiparameter regularization for Volterra kernel identification via multiscale collocation methods. Adv Comput Math 31, 421 (2009). https://doi.org/10.1007/s10444-008-9077-4
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DOI: https://doi.org/10.1007/s10444-008-9077-4