### Generalized quasilinearization method and higher order of convergence for second-order boundary value problems.

Melton, Tanya G., Vatsala, A.S. (2006)

Boundary Value Problems [electronic only]

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Melton, Tanya G., Vatsala, A.S. (2006)

Boundary Value Problems [electronic only]

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De Malafosse, Bruno (2003)

International Journal of Mathematics and Mathematical Sciences

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Babakhani, A., Enteghami, E. (2009)

Abstract and Applied Analysis

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Aghalary, R., Ebadian, A. (2009)

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De Malafosse, Bruno (2004)

International Journal of Mathematics and Mathematical Sciences

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de Malafosse, Bruno (2003)

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Siegfried Graf, Harald Luschgy, Gilles Pagès (2008)

ESAIM: Probability and Statistics

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We elucidate the asymptotics of the -quantization error induced by a sequence of -optimal -quantizers of a probability distribution on ${\mathbb{R}}^{d}$ when . In particular we show that under natural assumptions, the optimal rate is preserved as long as (and for every in the case of a compactly supported distribution). We derive some applications of these results to the error bounds for quantization based cubature formulae in numerical integration on ${\mathbb{R}}^{d}$ and on the Wiener space.

Alzer, H. (1993)

Acta Mathematica Universitatis Comenianae. New Series

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Plubtieng, Somyot, Punpaeng, Rattanaporn (2005)

International Journal of Mathematics and Mathematical Sciences

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