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A Note on Q-order of Convergence

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Abstract

To complement the property of Q-order of convergence we introduce the notions of Q-superorder and Q-suborder of convergence. A new definition of exact Q-order of convergence given in this note generalizes one given by Potra. The definitions of exact Q-superorder and exact Q-suborder of convergence are also introduced. These concepts allow the characterization of any sequence converging with Q-order (at least) 1 by showing the existence of a unique real number q ∈ [1,+∞] such that either exact Q-order, exact Q-superorder, or exact Q-suborder q of convergence holds.

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Authors and Affiliations

  1. Department of Mathematics, The University of Iowa, 14 MacLean Hall, Iowa City, IA, 52242-1419, USA

    L. O. Jay

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  1. L. O. Jay
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Jay, L.O. A Note on Q-order of Convergence. BIT Numerical Mathematics 41, 422–429 (2001). https://doi.org/10.1023/A:1021902825707

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  • DOI: https://doi.org/10.1023/A:1021902825707

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