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- W1985502054 abstract "This paper concerns the inverse problem of constructing the n-by-n real symmetric tridiagonal matrices C and K so that the monic quadratic pencil Q(λ) := λ2I + λC + K (where I is the identity matrix) possesses the given partial eigendata. We first provide the sufficient and necessary conditions for the existence of an exact solution to the inverse problem from the self-conjugate set of prescribed four eigenpairs. To find a physical solution for the inverse problem where the matrices C and K are weakly diagonally dominant and have positive diagonal elements and negative off-diagonal elements, we consider the inverse problem from the partial measured noisy eigendata. We propose a regularized smoothing Newton method for solving the inverse problem. The global and quadratic convergences of our approach are established under some mild assumptions. Some numerical examples and a practical engineering application in vibrations show the efficiency of our method." @default.
- W1985502054 created "2016-06-24" @default.
- W1985502054 creator A5055283405 @default.
- W1985502054 date "2007-12-20" @default.
- W1985502054 modified "2023-09-25" @default.
- W1985502054 title "Symmetric tridiagonal inverse quadratic eigenvalue problems with partial eigendata" @default.
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- W1985502054 doi "https://doi.org/10.1088/0266-5611/24/1/015005" @default.
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