Geodesic
Successive approximation by spaces of local functions
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part V, Tome 111 (1981), pp. 31-51

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One considers interpolation and approximation by local functions on a nonuniform net and stable algorithms for their successive construction. One introduces the concept of $H$-stability of a family of interpolations and one determines sufficient conditions for $H$-stability. One constructs nonhomogeneous spaces of local functions which realize an a priori approximation of a given order; the basis functions of these spaces have in a certain sense a minimal support and possess interpolation properties. 
@article{ZNSL_1981_111_a1,
     author = {Yu. K. Dem'yanovich},
     title = {Successive approximation by spaces of local functions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {31--51},
     publisher = {mathdoc},
     volume = {111},
     year = {1981},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1981_111_a1/}
}
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Yu. K. Dem'yanovich. Successive approximation by spaces of local functions. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part V, Tome 111 (1981), pp. 31-51. http://geodesic.mathdoc.fr/item/ZNSL_1981_111_a1/