| Summary: | 碩士 === 國立臺灣海洋大學 === 輪機工程學系 === 103 === Many problems in engineering can be categorized into linear systems but it is hard to solve the inverse problem because the solution is usually unstable. For instance, the ill-posed matrix problem or measurement with noise disturbance always leads to difficulty for solving; therefore, how to solve the inverse problem effectively and stably is the main objective of this thesis. To this point, the Optimal Multi-Vector Iterative Algorithm (OMVIA) is applied to Krylov Subspace Iteration Method, Double Optimal Iterative Algorithm (DOIA) and Double Optimal Regularization Algorithms (DORA). In the operation stage, the Arnoldi processing is adopted into the iteration algorithm yielded by Gram-Schmidt orthogonalzed to construct the matrix for solving the inverse problems. Several benchmark examples like the External force recovery problem, Duffing oscillator, Van Der Pol oscillator and Bouc-Wen model are conducted to validate the reliability and effectiveness of the proposed scheme.
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