The Budan-Fourier theorem for splines

Avraham A. Melkman

doi:10.1007/BF02757722

The Budan-Fourier theorem for splines

Avraham A. Melkman

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

The Budan-Fourier theorem for polynomials connects the number of zeros in an interval with the number of sign changes in the sequence of successive derivatives evaluated at the end-points. An extension is offered to splines with knots of arbitrary multiplicities, in which case the connection involves the number of zeros of the highest derivative. The theorem yields bounds on the number of zeros of splines and is a valuable tool in spline interpolation and approximation with boundary conditions.

Original language	English
Pages (from-to)	256-263
Number of pages	8
Journal	Israel Journal of Mathematics
Volume	19
Issue number	3
DOIs	https://doi.org/10.1007/BF02757722
State	Published - 1 Sep 1974
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

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10.1007/BF02757722

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The Budan-Fourier theorem for splines

Abstract

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