The Budan-fourier Theorem and Hermite-birkhoff Spline Interpolation
نویسنده
چکیده
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.
منابع مشابه
Cardinal interpolation and spline functions VIII. The Budan–Fourier Theorem for splines and applications
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