Please use this identifier to cite or link to this item: https://doi.org/10.1137/S0036142901393814
Title: Strong semismoothness of eigenvalues of symmetric matrices and its application to inverse eigenvalue problems
Authors: Sun, D. 
Sun, J. 
Keywords: Eigenvalues
Inverse eigenvalue problems
Newton's method
Quadratic convergence
Strong semismoothness
Symmetric matrices
Issue Date: 2002
Source: Sun, D.,Sun, J. (2002). Strong semismoothness of eigenvalues of symmetric matrices and its application to inverse eigenvalue problems. SIAM Journal on Numerical Analysis 40 (6) : 2352-2367. ScholarBank@NUS Repository. https://doi.org/10.1137/S0036142901393814
Abstract: It is well known that the eigenvalues of a real symmetric matrix are not everywhere differentiable. A classical result of Ky Fan states that each eigenvalue of a symmetric matrix is the difference of two convex functions, which implies that the eigenvalues are semismooth functions. Based on a recent result of the authors, it is further proved in this paper that the eigenvalues of a symmetric matrix are strongly semismooth everywhere. As an application, it is demonstrated how this result can be used to analyze the quadratic convergence of Newton's method for solving inverse eigenvalue problems (IEPs) and generalized IEPs with multiple eigenvalues.
Source Title: SIAM Journal on Numerical Analysis
URI: http://scholarbank.nus.edu.sg/handle/10635/44233
ISSN: 00361429
DOI: 10.1137/S0036142901393814
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