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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.

MSC:
41A05 Interpolation in approximation theory
41A15 Spline approximation
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