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

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High Performance Algorithms and Software for Nonlinear Optimization

Part of the book series: Applied Optimization ((APOP,volume 82))

Abstract

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 A ∈ R 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.

This work was supported by MIUR, National Research Program Algorithms for Complex Systems Optimization

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Author information

Authors and Affiliations

  1. Dipartimento di Informatica e Sistemistica “Antonio Ruberti”, Università di Roma “La Sapienza”, via Buonarroti 12, 00185, Roma, Italy

    Giovanni Fasano

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  1. Giovanni Fasano
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Editor information

Editors and Affiliations

  1. Università di Roma “La Sapienza”, Italy

    Gianni Di Pillo

  2. Università di Napoli Federico II, Italy

    Almerico Murli

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© 2003 Kluwer Academic Publishers B.V.

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Fasano, G. (2003). Planar-CG Methods and Matrix Tridiagonalization in Large Scale Unconstrained Optimization. In: Di Pillo, G., Murli, A. (eds) High Performance Algorithms and Software for Nonlinear Optimization. Applied Optimization, vol 82. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0241-4_11

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  • DOI: https://doi.org/10.1007/978-1-4613-0241-4_11

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-7956-0

  • Online ISBN: 978-1-4613-0241-4

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