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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14 citations
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TL;DR: In this paper, the Cubic Spline Super Fractal Interpolation Function (SFIF) is introduced to simulate an object that depicts one structure embedded into another and its approximation properties are investigated.
Abstract: In the present work, the notion of Cubic Spline Super Fractal Interpolation Function (SFIF) is introduced to simulate an object that depicts one structure embedded into another and its approximation properties are investigated. It is shown that, for an equidistant partition points of [x0, xN], the interpolating Cubic Spline SFIF and their derivatives converge respectively to the data generating function y(x) ≡ y(0)(x) and its derivatives y(j)(x) at the rate of h2-j+ϵ(0 < ϵ < 1), j = 0, 1, 2, as the norm h of the partition of [x0, xN] approaches zero. The convergence results for Cubic Spline SFIF found here show that any desired accuracy can be achieved in the approximation of a regular data generating function and its derivatives by a Cubic Spline SFIF and its corresponding derivatives.
14 citations
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TL;DR: An active set based algorithm for calculating the coefficients of univariate cubic L1 splines is developed that outperforms a currently widely used discretization-based primal affine algorithm.
Abstract: An active set based algorithm for calculating the coefficients of univariate cubic L1 splines is developed. It decomposes the original problem in a geometric-programming setting into independent optimization problems of smaller sizes. This algorithm requires only simple algebraic operations to obtain an exact optimal solution in a finite number of iterations. In stability and computational efficiency, the algorithm outperforms a currently widely used discretization-based primal affine algorithm.
14 citations
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TL;DR: In this paper, conditions are given which ensure that the solution has no poles between the points of interpolation, and comparison theorems on the error of the interpolation are also derived.
Abstract: This paper is concerned with interpolation by rational functions. Conditions are given which ensure that the solution has no poles between the points of interpolation. Comparison theorems on the error of the interpolation are also derived.
14 citations