Showing papers on "Monotone cubic interpolation published in 2018"
TL;DR: A new optimal cubic Hermite interpolation method is presented to optimize the derivative of the interpolant and the diagonally dominant property of the obtained system of normal equations and the error bound are better than some of the existing cubic interpolants.
26 citations
TL;DR: This paper presents cubic G 1 Hermite interpolation by minimizing curvature variation energy subject to a feasible region, with the advantage of handling arbitrary G 1 data.
19 citations
TL;DR: A new numerical approach for finding the solution of linear time‐delay control systems with a quadratic performance index using new hybrid functions based on a hybrid of block‐pulse functions and biorthogonal multiwavelets that consist of cubic Hermite splines on the primal side.
15 citations
01 Jul 2018
TL;DR: A fast interpolation method by cubic B-spline for parametric curve interpolation is presented which results in a minimum feedrate fluctuation and light computation load and can attain high accuracy and computation efficiency.
Abstract: Due to the reliable feedrate fluctuation and computation load of the existing parametric curve interpolation, a fast interpolation method by cubic B-spline for parametric curve is presented which r...
12 citations
TL;DR: In this article, a rational cubic fractal interpolant is used to generate surfaces that lie above a prescribed straight line, and a transfinite interpolation via blending functions is proposed to preserve positivity inherent in a prescribed data set.
Abstract: This paper investigates some univariate and bivariate constrained interpolation problems using fractal interpolation functions. First, we obtain rational cubic fractal interpolation functions lying above a prescribed straight line. Using a transfinite interpolation via blending functions, we extend the properties of the univariate rational cubic fractal interpolation function to generate surfaces that lie above a plane. In particular, the constrained bivariate interpolation discussed herein includes a method to construct fractal interpolation surfaces that preserve positivity inherent in a prescribed data set. Uniform convergence of the bivariate fractal interpolant to the original function which generates the data is proven.
11 citations
TL;DR: In this article, a numerical method is proposed for the numerical solution of a linear system with suitable initial and boundary conditions using the cubic B-spline collocation scheme to determine th...
Abstract: In this paper, a numerical method is proposed for the numerical solution of a linear system with suitable initial and boundary conditions using the cubic B-spline collocation scheme to determine th...
10 citations
TL;DR: A class of rational quartic/cubic interpolation spline with two local control parameters is presented, which can be C 2 continuous without solving a linear system of consistency equations for the derivative values at the knots.
9 citations
01 Oct 2018
TL;DR: An improved approach to the CSI scheme is proposed for the decimation and interpolation of image data and computer simulations indicate that the proposed CSI scheme can achieve better performance without increasing the computational complexity compared with the four-point CSI scheme.
Abstract: Cubic-spline interpolation (CSI) scheme is known to resample the discrete image data based on the least-square method with the cubic convolution interpolation (CCI) function. It is superior in performance to other interpolation functions for digital image processing. In this paper, an improved approach to the CSI scheme is proposed for the decimation and interpolation of image data. The proposed CSI scheme combines the least-square method with six-point CCI function to improve performance. Moreover, a novel low-complexity implementation algorithm is proposed to simplify the decimation and achieve improvement of the computational efficiency. Computer simulations indicate that the proposed CSI scheme can achieve better performance without increasing the computational complexity compared with the four-point CSI scheme.
9 citations
TL;DR: A class of cubic trigonometric interpolation spline curves with two parameters that can automatically interpolate the given data points and become C ² 2 interpolation curves without solving equations system even if the interpolation conditions are fixed.
Abstract: A class of cubic trigonometric interpolation spline curves with two parameters is presented in this paper. The spline curves can automatically interpolate the given data points and become C ² 2 interpolation curves without solving equations system even if the interpolation conditions are fixed. Moreover, shape of the interpolation spline curves can be globally adjusted by the two parameters. By selecting proper values of the two parameters, the optimal interpolation spline curves can be obtained.
9 citations
TL;DR: It is proved that a spline space of this class of all piecewise Chebyshevian splines with connection matrices at the knots is “good for interpolation” if and only if thespline space obtained by integration is "good for design”.
Abstract: We consider the wide class of all piecewise Chebyshevian splines with connection matrices at the knots We prove that a spline space of this class is “good for interpolation” if and only if the spline space obtained by integration is “good for design” As a consequence, this provides us with a simple practical description of all such spline spaces which can be used for solving Hermite interpolation problems These results strongly rely on the properties of blossoms
4 citations
TL;DR: In this paper, Hermite interpolation by parametric spline surfaces on triangulations is considered and two variations of the scheme are studied: C1 quintic and G1 octic.
Abstract: In this paper, Hermite interpolation by parametric spline surfaces on triangulations is considered. The splines interpolate points, the corresponding tangent planes and normal curvature forms at domain vertices and approximate tangent planes at midpoints of domain edges. Two variations of the scheme are studied: C1 quintic and G1 octic. The latter is of higher polynomial degree but can approximate surfaces of arbitrary topology. The construction of the approximant is local and fast. Some numerical examples of surface approximation are presented.
TL;DR: In this article, the authors proposed an alternative to cubic spline regularization and its weighted form applied in solving inverse thermal problems, which is able to enhance filter action and improve flexibility and accuracy.
Abstract: This paper presents an alternative to cubic spline regularization and its weighted form applied in solving inverse thermal problems. The inverse heat transfer problems are classified as ill-posed, that is, the solution may become unstable, mainly because they are sensitive to random errors deriving from the input data, necessitating a regularization method to soften these effects. The smoothing technique proposed by cubic spline regularization ensures that the global data tend to be more stable, with fewer data oscillations and dependent on a single arbitrary parameter input. It also shows that the weighted cubic spline is able to enhance filter action. The methods have been implemented in order for the search engine to optimize the choice of parameters and weight and, thus, the smoothing gains more flexibility and accuracy. The simulated and experimental tests confirm that the techniques are effective in reducing the amplified noise by inverse thermal problem presented.