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Siberian Journal of Numerical Mathematics

2017 year, number 4

The Lebesgue constant of local cubic splines with equally-spaced knots

V.T. Shevaldin1, O.Ya. Shevaldina2
1Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, S. Kovalevskaja st., 16, Ekaterinburg, Russia, 620990
2Ural Federal University, 19 Mira street, Ekaterinburg, Russia, 620002
Keywords: константа Лебега, локальные кубические сплайны, равноотстоящие узлы, Lebesgue constants, local cubic splines, equally-spaced knots

Abstract

It is proved that the uniform Lebesgue constant (the norm of a linear operator from C to C) of local cubic splines with equally-spaced knots, which preserve cubic polynomials, is equal to 11/9.