Geodesic
The inverses of cyclic band matrices and the convergence of interpolation processes for derivatives of periodic interpolation splines
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 13 (2010) no. 3, pp. 243-253

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The estimates for entries of matrices inverse to the cyclic band matrices and for the matrix norms are presented. The results obtained are used for determining the convergence conditions of Interpolation processes by periodic odd degree splines for different derivatives. In particular, the positive solution to the C. de Boor problem on unconditional convergence of one of the two middle derivatives in the periodic case is proposed. 
@article{SJVM_2010_13_3_a0,
     author = {Yu. S. Volkov},
     title = {The inverses of cyclic band matrices and the convergence of interpolation processes for derivatives of periodic interpolation splines},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {243--253},
     publisher = {mathdoc},
     volume = {13},
     number = {3},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2010_13_3_a0/}
}
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Yu. S. Volkov. The inverses of cyclic band matrices and the convergence of interpolation processes for derivatives of periodic interpolation splines. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 13 (2010) no. 3, pp. 243-253. http://geodesic.mathdoc.fr/item/SJVM_2010_13_3_a0/