Strong semismoothness of eigenvalues of symmetric matrices and its application to inverse eigenvalue problems

Defeng Sun, J. Sun

Research output: Journal article publicationJournal articleAcademic researchpeer-review

48 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)2352-2367
Number of pages16
JournalSIAM Journal on Numerical Analysis
Issue number6
Publication statusPublished - 1 Dec 2002
Externally publishedYes


  • Eigenvalues
  • Inverse eigenvalue problems
  • Newton's method
  • Quadratic convergence
  • Strong semismoothness
  • Symmetric matrices

ASJC Scopus subject areas

  • Numerical Analysis

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