Computing for eigenpairs on globally convergent iterative method for hermitian matrices

  • Authors:

  • Ran Baik;Karabi Datta;Yoopyo Hong

  • Affiliations:

  • Department of Computer Engineering, Honam University, Gwangju, Korea;Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL;Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL

  • Venue:
  • ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part I
  • Year:
  • 2005

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Abstract

Let A = A* ∈ Mn and ${\cal L} = \{ (U_k, \lambda_k)|\; U_k \in {\mathbb{C}}^n, ||U_k|| = 1$ and λk∈ℝ } for k = 1,⋯,n be the set of eigenpairs of A. In this paper we develop a modified Newton method that converges to a point in $\cal L$ starting from any point in a compact subset ${\cal D} \subseteq {\mathbb{C}}^{n+1}, {\cal L} \subseteq {\cal D}\!$.