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Asymptotic Rate of Convergence of a Two-Layer Iterative Method of the Variational Type

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We present the definition and study the dependence on the initial approximation of the asymptotic rate of convergence of a two-layer symmetrizable iterative method of the variational type. The explicit expression is obtained for the substantial (with respect to the Lebesgue measure) range of its values. Its domain of continuity is described.

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Correspondence to P. F. Zhuk.

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, No. 12, pp. 1622–1635, December, 2013.

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Zhuk, P.F., Musina, A.A. Asymptotic Rate of Convergence of a Two-Layer Iterative Method of the Variational Type. Ukr Math J 65, 1793–1808 (2014). https://doi.org/10.1007/s11253-014-0898-7

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  • Lebesgue Measure
  • Initial Approximation
  • Steep Descent
  • Variational Type
  • Iterative Sequence