Topic
Monotone cubic interpolation
About: Monotone cubic interpolation is a research topic. Over the lifetime, 1740 publications have been published within this topic receiving 38111 citations.
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TL;DR: In this paper, an efficient high order numerical method based on cubic spline approximation and application of alternating group explicit method for the solution of two point non-linear boundary value problems, whose forcing functions are in integral form, on a non-uniform mesh.
13 citations
TL;DR: In this article, the authors established a new computing method for the cubic spline difference, which is characterized by the simplicity of the finite difference method through discussion of various heat conduction problems.
13 citations
TL;DR: A high-order full-discretization method using Hermite interpolation (HFDM) is proposed and implemented for periodic systems with time delay and shows that the proposed HFDM converges faster and uses less computational time than existing methods.
Abstract: A high-order full-discretization method (FDM) using Hermite interpolation (HFDM) is proposed and implemented for periodic systems with time delay. Both Lagrange interpolation and Hermite interpolation are used to approximate state values and delayed state values in each discretization step. The transition matrix over a single period is determined and used for stability analysis. The proposed method increases the approximation order of the semidiscretization method and the FDM without increasing the computational time. The convergence, precision, and efficiency of the proposed method are investigated using several Mathieu equations and a complex turning model as examples. Comparison shows that the proposed HFDM converges faster and uses less computational time than existing methods.
12 citations
TL;DR: A Lagrangian parameter approach to problems of best constrained approximation in Hilbert space is reviewed, which is applied to the problem of interpolation of data in a plane by a cubic spline function which is subject to obstacles.
Abstract: We review a Lagrangian parameter approach to problems of best constrained approximation in Hilbert space. The variable is confined to a closed convex subset of the Hilbert space and is also assumed to satisfy linear equalities. The technique is applied to the problem of interpolation of data in a plane by a cubic spline function which is subject to obstacles. The obstacles may be piecewise cubic polynomials over the original knot set. A characterization result is obtained which is used to develop a Newton-type algorithm for the numerical solution.
12 citations
TL;DR: Numerical tests indicate that the proposed piecewise bivariate Hermite interpolations are economic and have good approximation capacity.
Abstract: The requirements for interpolation of scattered data are high accuracy and high efficiency. In this paper, a piecewise bivariate Hermite interpolant satisfying these requirements is proposed. We firstly construct a triangulation mesh using the given scattered point set. Based on this mesh, the computational point () is divided into two types: interior point and exterior point. The value of Hermite interpolation polynomial on a triangle will be used as the approximate value if point () is an interior point, while the value of a Hermite interpolation function with the form of weighted combination will be used if it is an exterior point. Hermite interpolation needs the first-order derivatives of the interpolated function which is not directly given in scatted data, so this paper also gives the approximate derivative at every scatted point using local radial basis function interpolation. And numerical tests indicate that the proposed piecewise bivariate Hermite interpolations are economic and have good approximation capacity.
12 citations