Showing papers on "Monotone cubic interpolation published in 1977"
TL;DR: For a set of monotone (and/or convex) data, this article considered the possibility of finding a spline interpolant, of pre-determined smoothness, which is either monotonicity or convex.
Abstract: For a set of monotone (and/or convex) data, we consider the possibility of finding a spline interpolant, of pre-determined smoothness, which is monotone (and/or convex). The investigation is carried out by constructing an auxiliary set of points and using the well-known monotonicity and convexity preserving properties of Bernstein polynomials. In § 3 we consider the problem of piecewise monotone interpolation.
112 citations
TL;DR: Algorithms are presented for computing a smooth piecewise polynomial interpolation which preserves the monotonicity and/or convexity of the data.
Abstract: Algorithms are presented for computing a smooth piecewise polynomial interpolation which preserves the monotonicity and/or convexity of the data.
85 citations
TL;DR: In this article, it is shown that broken line interpolation as a scheme for piecewise monotone interpolation is hard to improve upon, and that a family of smooth piecewise polynomial interpolants, introduced by Swartz and Varga and noted by Passow to be piecewise non-linear, converges to a piecewise constant interpolant as the degree goes to infinity.
74 citations
TL;DR: In this article, the standard cubic spline regression method is shown to be a special case of the restricted least-squares estimator, and the equivalence of the two procedures under a common set of restrictions is proved.
Abstract: The standard cubic spline regression method is shown to be a special case of the restricted least-squares estimator. The equivalence of the two procedures under a common set of restrictions is proved. The greater flexibility of the restricted least-squares estimator in terms of the number of restrictions and tests of hypotheses that can be utilized is illustrated by an application to a set of data that has been previously analyzed by the spline method.
70 citations
TL;DR: In this paper, a method is presented for fitting a bivariate cubic spline function to values of a dependent variable, specified at points on a rectangular grid in the plane of the independent variables.
32 citations
26 citations
01 Jan 1977
TL;DR: By consideration of special ideals a n-dimensional generalization of Max Noether's theorem is obtained, which enables us to answer questions arising in the constructive theory of functions as it is shown by three examples.
Abstract: The ideal-theoretic concept of the Hermite interpolation was presented in [9]. Some of its results are summarized in this paper. By consideration of special ideals a n-dimensional generalization of Max Noether's theorem is obtained. This generalization enables us to answer questions arising in the constructive theory of functions as it is shown by three examples.
18 citations
TL;DR: In this article, it was shown that the Hermite-Birkhoff spline interpolation problem is poised, provided that the knots of the spline and the interpolation points interlace properly.
8 citations
8 citations
2 citations
09 May 1977
TL;DR: In this paper, a cubic spline (a piecewise cubic polynomial with two derivatives continuous at the joints) is fitted to a set of n equispaced data by exploiting the eigenfunction-eigenvalue expansion of a particular sparse matrix.
Abstract: A new method is presented for fitting a cubic spline (piecewise cubic polynomial with two derivatives continuous at the joints) to a set of n equispaced data. The method exploits the eigenfunction-eigenvalue expansion of a particular sparse matrix, and determines the piecewise polynomial coefficients in 2n\log_{2}n operations.
CERN1
01 Jan 1977