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On the relation between quadratic termination and convergence properties of minimization algorithms

Part II. Application

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Summary

It is shown that the theory developed in part I of this paper [22] can be applied to some well-known minimization algorithms with the quadratic termination property to prove theirn-step quadratic convergence. In particular, some conjugate gradient methods, the rank-1-methods of Pearson and McCormick (see Pearson [18]) and the large class of rank-2-methods described by Oren and Luenberger [16, 17] are investigated.

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Authors and Affiliations

  1. Institut für Angewandte Mathematik und Statistik der Universität Würzburg Am Hubland, D-8700, Würzburg, Germany (Fed. Rep.)

    P. Baptist & J. Stoer

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  1. P. Baptist
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  2. J. Stoer
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Additional information

This work was supported in part at Stanford University, Stanford, California, under Energy Research and Development Administration, Contract E(04-3) 326 PA No. 30, and National Science Foundation Grant DCR 71-01996 A04 and in part by the Deutsche Forschungsgemeinschaft

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Baptist, P., Stoer, J. On the relation between quadratic termination and convergence properties of minimization algorithms. Numer. Math. 28, 367–391 (1977). https://doi.org/10.1007/BF01404342

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