Planar-CG Methods and Matrix Tridiagonalization in Large Scale Unconstrained Optimization

  • Giovanni Fasano
Part of the Applied Optimization book series (APOP, volume 82)


In this paper we aim at carrying out and describing some issues for real eigenvalue computation via iterative methods. More specifically we work out new techniques for iteratively developing specific tridiagonalizations of a symmetric and indefinite matrix AR n × n , by means of suitable Krylov subspace algorithms defined in [16], [26]. These schemes represent extensions of the well known Conjugate Gradient (CG) method to the indefinite case. We briefly recall these algorithms and we suggest a comparison with the method in [22], along with a discussion on the practical application of the proposed results for eigenvalue computation. Furthermore, we focus on motivating the fruitful use of these tridiagonalizations for ensuring the convergence to second order points, within an optimization framework.


unconstrained optimization eigenvalue computation matrix tridiagonalization Conjugate Gradient Krylov subspace methods 


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Copyright information

© Kluwer Academic Publishers B.V. 2003

Authors and Affiliations

  • Giovanni Fasano
    • 1
  1. 1.Dipartimento di Informatica e Sistemistica “Antonio Ruberti”Università di Roma “La Sapienza”RomaItaly

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