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演講者:林敏雄 教授 (Department of Mathematics, National Cheng Kung University)

講題:On a Geometric Approach for Solving Structured Inverse Eigenvalue and Singular Value Problems

時間:01/08(二) 13:30


摘要:Inverse eigenvalue and singular value problems have been widely

      discussed for decades. The well-known result is the Weyl-Horn

      condition, which presents the relations between the eigenvalues

      and singular values of an arbitrary matrix. This result by

      Weyl-Horn then leads to an interesting inverse problem,

      i.e., how to construct a matrix with desired eigenvalues and

      singular values. In this talk, two topics will be included.

      First,we provide a necessary and sufficient condition for the

      existence of a 2-by-2 real matrix, or even a nonnegative matrix,

      with prescribed eigenvalues, singular values, and main diagonal

      entries.Second, we propose an eclectic mix of techniques from

      differential geometry and the inexact Newton method for solving

      inverse eigenvalue and singular value problems as well as

      additional desired characteristics such as nonnegative entries,

      prescribed diagonal entries, and even predetermined entries.

      We show theoretically that our method converges globally and

      quadratically,and we provide numerical examples to demonstrate

      the robustness and accuracy of our proposed method.

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