作者: 时间:2022-04-12 点击数:

报告时间:2022年4月15日  10:00

线上腾讯会议 633-553-762


报告题目:An inverse eigenvalue problem for pseudo-Jacobi matrices


In this talk, the theory on direct and inverse spectral problems for Jacobi matrices is revisited in a kind of pseudo-Jacobi matrices J (n, r, β) with a mixed path as its graph in the non-self-adjoint setting. In this context, a sign change in one of the nondiagonal entries of the matrix yields strong perturbations in its spectral properties. By analogy with van Moerbeke's construction idea for Jacobi matrices, the reconstruction of a pseudo-Jacobi matrix from its spectrum and the spectra of two complementary principal matrices is investigated. An algorithm for the reconstruction of matrices from prescribed spectral data is provided and illustrative numerical experiments are performed. Finally, an extended eigenvector-eigenvalue identity is introduced, and can be used to solve some other pseudo-Jacobi inverse eigenvalue problems. 



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