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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

On a posteriori error estimates


Author: George Miel
Journal: Math. Comp. 31 (1977), 204-213
MSC: Primary 65J05
MathSciNet review: 0426418
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Abstract: Consider a sequence $ \{ {x_n}\} _{n = 0}^\infty $ in a normed space X converging to some $ {x^\ast} \in X$. It is shown that the sequence satisfies a condition of the type

$\displaystyle \left\Vert {{x^\ast} - {x_n}} \right\Vert \leqslant \alpha \left\Vert {{x_n} - {x_{n - 1}}} \right\Vert$

for some constant $ \alpha $ and every $ n \geqslant 1$, if the associated null sequence $ \{ {e_n}\} _{n = 0}^\infty ,{e_n} = {x^\ast} - {x_n}$ , is uniformly decreasing in norm or if it is alternating with respect to any ordering whose cone of positive elements is acute.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1977-0426418-4
PII: S 0025-5718(1977)0426418-4
Keywords: A posteriori error estimates
Article copyright: © Copyright 1977 American Mathematical Society