Third-order accurate monotone cubic Hermite interpolants

Aràndiga, Francesc; Yáñez, Dionisio F.

doi:10.1016/j.aml.2019.02.012

Cited by 7 publications

(9 citation statements)

References 10 publications

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“…In this case the value ḟ F B i is defined in a way that automatically satisfies (5). If f is smooth and…”

Section: Non-linear Computation Of Derivativesmentioning

confidence: 99%

“…Brodlie's formula produces a third order interpolant only in the case of using equally-spaced grids. In [5] (see also [3]) Aràndiga and Yáñez introduce a new method to compute the approximated derivatives based on the weighted harmonic mean that achieve third order of accuracy for non-uniform grids and preserves monotonicity. The proposed formula is:…”

Section: Non-linear Computation Of Derivativesmentioning

confidence: 99%

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Monotone cubic spline interpolation for functions with a strong gradient

Aràndiga,

Baeza,

Yáñez

2021

Preprint

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Spline interpolation has been used in several applications due to its favorable properties regarding smoothness and accuracy of the interpolant. However, when there exists a discontinuity or a steep gradient in the data, some artifacts can appear due to the Gibbs phenomenon. Also, preservation of data monotonicity is a requirement in some applications, and that property is not automatically verified by the interpolator. In this paper, we study sufficient conditions to obtain monotone cubic splines based on Hermite cubic interpolators and propose different ways to construct them using non-linear formulas. The order of approximation, in each case, is calculated and several numerical experiments are performed to contrast the theoretical results.

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“…In this case the value ḟ F B i is defined in a way that automatically satisfies (5). If f is smooth and…”

Section: Non-linear Computation Of Derivativesmentioning

confidence: 99%

Section: Non-linear Computation Of Derivativesmentioning

confidence: 99%

Monotone cubic spline interpolation for functions with a strong gradient

Aràndiga,

Baeza,

Yáñez

2021

Preprint

Self Cite

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“…Example 3. In this example, the sample data set from the research [24] was used ( Table 5). The results of the algorithm are shown in Figure 3.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…In this research work, an iterative algorithm for calculating derivatives at the interpolation points was constructed to build a monotone interpolant, which guarantees the function monotonicity on the interval for non-uniform data sets. In [24], the method of calculating the derivatives at the interpolation points as a weighted harmonic average was used to construct monotone interpolation methods.…”

Section: Introductionmentioning

confidence: 99%

“…Results of the spline curve calculation for data from[24] Results of the spline curve calculation for an arbitrary sequence of control points. There are many studies on the approach of conical sections, see, for example[27].Here we demonstrate the possibility for the approximation of the ellipse using the proposed curve = 2 cos , = sin , = 0points, tangent ones are constructed.…”

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confidence: 99%

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Computer Realizations of the Cubic Parametric Spline Curve of Bèzier Type

Stelia¹,

Potapenko²,

Sirenko³

2019

IJC

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This paper presents a new method for constructing a third degree parametric spline curve of C1 continuity. Like the Bèzier curve, the proposed curve is constructed and operated by control points. The peculiarity of the proposed algorithm is the assignment of some unknown values of the spline in the control points abscissas, which are based on the conditions of the first derivative continuity of the curve at these points. The position of the touch points, as well as the control points, can be set interactively. Changing of these points positions leads to a change in the curve shape. This allows the user to flexibly adjust the shape of the curve. Systems of algebraic equations with tridiagonal matrix for calculating the coefficients of a spline curve are constructed. Conditions for the existence and uniqueness of such a curve are presented. Examples of the use of the proposed curve, in particular, for monotone data sets, approximation the ellipse and constructing the letter "S" are given.

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