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Quasi-interpolants from spline interpolation operators. (English) Zbl 0683.41009
Summary: For bi-infinite Toeplitz matrices, it is easy to see that the k-th partial sum of the Neumann series reproduces polynomials of order k. There is no guarantee, however, that the spectral radius is less than 1. A principal result of this paper is to show that for the spline interpolation Toeplitz case the spectral radius is less than 1 when A is invertible and the main diagonal is the central diagonal. This is not true for all totally positive Toeplitz matrices as shown by an example in Section 2.

41A05 Interpolation in approximation theory
41A15 Spline approximation
Full Text: DOI
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