The Budan-Fourier theorem and Hermite-Birkhoff spline interpolation

Goodman, T. N. T.; Lee, S. L.

doi:10.1090/S0002-9947-1982-0654844-5

The Budan-Fourier theorem and Hermite-Birkhoff spline interpolation
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by T. N. T. Goodman and S. L. Lee PDF

Trans. Amer. Math. Soc. 271 (1982), 451-467 Request permission

Abstract:

We extend the classical Budan-Fourier theorem to Hermite-Birkhoff splines, that is splines whose knots are determined by a finite incidence matrix. This is then applied to problems of interpolation by Hermite-Birkhoff splines, where the nodes of interpolation are also determined by a finite incidence matrix. For specified knots and nodes in a finite interval, conditions are examined under which there is a unique interpolating spline for any interpolation data. For knots and nodes spaced periodically on the real line, conditions are examined under which there is a unique interpolating spline of power growth for data of power growth.

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