Summary.
In this paper, we study the inverse eigenvalue problem of a specially structured Jacobi matrix, which arises from the discretization of the differential equation governing the axial of a rod with varying cross section (Ram and Elhay 1998 Commum. Numer. Methods Engng. 14 597-608). We give a sufficient and some necessary conditions for such inverse eigenvalue problem to have solutions. Based on these results, a simple method for the reconstruction of a Jacobi matrix from eigenvalues is developed. Numerical examples are given to demonstrate our results.
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Research supported in part by National Natural Science Foundation of China
Research supported in part by RGC Grant Nos. 7130/02P and 7046/03P, and HKU CRCG Grant Nos 10203501, and 10204437
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Lu, L., Ng, M. On sufficient and necessary conditions for the Jacobi matrix inverse eigenvalue problem. Numer. Math. 98, 167–176 (2004). https://doi.org/10.1007/s00211-004-0525-x
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DOI: https://doi.org/10.1007/s00211-004-0525-x