Geodesic
On orthorecursive expansions with errors in the calculation of coefficients
Izvestiya. Mathematics , Tome 69 (2005) no. 1, pp. 1-14

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We study orthorecursive expansions with errors in the calculation of coefficients. We prove that if a system of elements in a space with scalar product satisfies certain requirements, then the orthorecursive expansion with respect to this system is absolutely stable under a large class of relative and absolute numerical errors. It is also stable under small perturbations of the system. 
@article{IM2_2005_69_1_a0,
     author = {V. V. Galatenko},
     title = {On orthorecursive expansions with errors in the calculation of coefficients},
     journal = {Izvestiya. Mathematics },
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2005_69_1_a0/}
}
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V. V. Galatenko. On orthorecursive expansions with errors in the calculation of coefficients. Izvestiya. Mathematics , Tome 69 (2005) no. 1, pp. 1-14. http://geodesic.mathdoc.fr/item/IM2_2005_69_1_a0/