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Article

Vejchodský, Tomáš
Complementarity - the way towards guaranteed error estimates. (English). In: Chleboun, J., Přikryl, P., Segeth, K. and Šístek, J. (eds.): Programs and Algorithms of Numerical Mathematics. Proceedings of Seminar. Dolní Maxov, June 6-11, 2010. Institute of Mathematics AS CR, Prague, 2010. pp. 205-220
MSC: 65N15, 65N30
Keywords:
complementarity; guaranteed upper error bounds; method of hypercircle; a posteriori error estimates; error majorants
Summary:
This paper presents a review of the complementary technique with the emphasis on computable and guaranteed upper bounds of the approximation error. For simplicity, the approach is described on a numerical solution of the Poisson problem. We derive the complementary error bounds, prove their fundamental properties, present the method of hypercircle, mention possible generalizations and show a couple of numerical examples.
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