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 article, the notions of R-intersection, R-union, Pintersection and P-union of cubic linear spaces are defined and some results on these are provided.
Abstract: The main motivation of this paper is to introduce the notion of cubic linear space. This inspiration is received from the structure of cubic sets. The notions of R-intersection, R-union, P-intersection, and P-union of cubic linear spaces are defined and we provide some results on these. We further introduce the notion of internal cubic linear space and external cubic linear space and establish some results on them.
8 citations
TL;DR: In this paper, a modular collocation approach with the cubic spline interpolation function is developed and applied to an underlying distillation model which is constructed based on the McCabe and Thiele assumptions plus constant tray holdups.
Abstract: A simple and compact form of reduced-order distillation model especially suitable for real-time applications is proposed. For this purpose, a modular collocation approach with the cubic spline interpolation function is developed and applied to an underlying distillation model which is constructed based on the McCabe and Thiele assumptions plus constant tray holdups. To evaluate the performance of the model, numerical simulations are carried out for the case of dynamics as well as steady states. As a consequence, it is found that the proposed reduced-order model gives better approximation than those obtained by the conventional reduced-order model with the Lagrange interpolation function.
8 citations
TL;DR: In this paper, an eigenvalue analysis of the first-order Hermite cubic spline collocation differentiation matrices with arbitrary collocation points is presented and compared with some other discrete methods, such as finite difference methods.
Abstract: In this paper, we present an eigenvalue analysis of the first-order Hermite cubic spline collocation differentiation matrices with arbitrary collocation points. Some important features are explored and the method is compared with some other discrete methods, such as finite difference methods. A class of spline collocation methods with upwind features is proposed for solving singular perturbation problems.
8 citations
TL;DR: In this article, the authors consider the spline-on-spline technique for calculating the derivative of a function from its values on a uniform mesh and derive new consistency relations between a cubic spline and a cubic interpolation of its first derivative.
8 citations
8 citations