Interpolation and approximation by monotone cubic splines
نویسندگان
چکیده
منابع مشابه
Constrained Interpolation via Cubic Hermite Splines
Introduction In industrial designing and manufacturing, it is often required to generate a smooth function approximating a given set of data which preserves certain shape properties of the data such as positivity, monotonicity, or convexity, that is, a smooth shape preserving approximation. It is assumed here that the data is sufficiently accurate to warrant interpolation, rather than least ...
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In this paper, geometric interpolation by G cubic spline is studied. A wide class of sufficient conditions that admit a G cubic spline interpolant is determined. In particular, convex data as well as data with inflection points are included. The existence requirements are based upon geometric properties of data entirely, and can be easily verified in advance. The algorithm that carries out the ...
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We prove that the degree of shape preserving free knot spline approximation in L p a; b], 0 < p 1 is essentially the same as that of the non-constrained case. This is in sharp contrast to the well known phenomenon we have in shape preserving approximation by splines with equidistant knots and by polynomials. The results obtained are valid both for piecewise polynomials and for smooth splines wi...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1991
ISSN: 0021-9045
DOI: 10.1016/0021-9045(91)90033-7