Shape determination for deformed electromagnetic cavities
Journal of Computational Physics
Minimizing the Condition Number of a Gram Matrix
SIAM Journal on Optimization
Approximation of rank function and its application to the nearest low-rank correlation matrix
Journal of Global Optimization
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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.