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
Patent•
29 Sep 1989TL;DR: In this article, a spline interpolation system which interpolates a given point by a cubic spline curve is described. But this is not a practical problem, since the line of all the points at a time is unknown.
Abstract: This invention relates to a spline interpolation system which interpolates a given point by a cubic spline curve. A linear differential vector is determined from a predetermined number of points including a start point (P1) and a cubic equation between the start point (P1) and a next point (P2) is determined from the coordinates value of predetermined points including the start point (P1) and the end condition of the start point (P1). Then, a spline curve between the start point (P1) and the next point (P2) continuing from the former is determined. Next, a spline curve between points P2 and P3 is determined by adding the linear differential vector at a new point in place of the start point (P1) and (P2). In this manner, the cubic equations between points are obtained sequentially and a cubic spline curve is obtained. A spline curve free from a practical problem can be determined by sequentially reading points starting with the first without reading in advance the line of all the points at a time.
14 citations
TL;DR: A local convexity preserving interpolation scheme using parametricC2 cubic splines with uniform knots produced by a vector subdivision scheme which simultaneously provides the function and its first and second order derivatives is given.
Abstract: We give a local convexity preserving interpolation scheme using parametricC2 cubic splines with uniform knots produced by a vector subdivision scheme which simultaneously provides the function and its first and second order derivatives. This is also adapted to give a scheme which is both local convexity and local monotonicity preserving when the data values are strictly increasing in thex-direction.
14 citations
TL;DR: A difference scheme based on cubic spline in tension for second-order singularly perturbed boundary-value problem of the form λ1 and λ2 is considered and the method is tested and the results are found to be in agreement with the theory.
Abstract: We consider a difference scheme based on cubic spline in tension for second-order singularly perturbed boundary-value problem of the form The method is shown to have second- and fourth-order convergence depending on the choice of parameters λ1 and λ2 involved in the method. The method is tested on an example and the results found to be in agreement with the theory.
14 citations
TL;DR: In this article, a new Shepard-type operator of degree of exactness greater than zero was constructed by using bivariate Taylor, Lagrange or Hermite interpolation operators, which is known as the Birkhoff interpolation operator.
Abstract: :It is known that the Shepard interpolation operator has degree of exactness zero. In papers [1, 4–6] new Shepard-type operators of degree of exactness greater than zero were constructed by using bivariate Taylor, Lagrange or Hermite interpolation operators. In this note such a Shepard-type operator is constructed by using bivariate Birkhoff interpolation operators.
14 citations