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On theR-order of coupled sequences arising in single-step type methods

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Summary

As shown in preceding papers of the authors, the verification of anR-convergence order τ for sequences coupled by a system (1.1) of basic inequalities can be reduced to the positive solvability of system (3.3) of linear inequalities. Further, the bestR-order\(\bar \tau\) implied by (1.1) is equal to the minimal spectral radius of certain matrices composed from the exponents occuring in (1.1). Now, these results are proven in a unified and essentially simpler way. Moreover, they are somewhat extended in order to facilitate applications to concrete methods.

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Authors and Affiliations

  1. Department of Mathematics, Technical University of Dresden, Mommsenstrasse 13, DDR-8027, Dresden, German Democratic Republic

    W. Burmeister & J. W. Schmidt

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  1. W. Burmeister
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  2. J. W. Schmidt
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Burmeister, W., Schmidt, J.W. On theR-order of coupled sequences arising in single-step type methods. Numer. Math. 53, 653–661 (1988). https://doi.org/10.1007/BF01397134

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  • DOI: https://doi.org/10.1007/BF01397134

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