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, the authors presented a new iterative method, derived from Hermite interpolation, with order of convergence p = 1+, which requires, at each step, only two function evaluations, which is better than those of classical methods, such as the secant method or Newton's method, and those of the recent methods introduced by Costabile et al.
Abstract: We present a new iterative method, derived from Hermite interpolation, with order of convergence p = 1+ , which requires, at each step, only two function evaluations. The efficiency index of the method is better than those of classical methods, such as the secant method or Newton's method, and those of the recent methods introduced by Costabile et al. [1,2] as well. This method has the best efficiency index in a family of methods derived from Hermite interpolation.
24 citations
TL;DR: This work introduces the addition of lines as a way of constructing lattices generated by cubic pencils, which has the same good properties and simple formulae as on principal lattices.
Abstract: Principal lattices are distributions of points in the plane obtained from a triangle by drawing equidistant parallel lines to the sides and taking the intersection points as nodes. Interpolation on principal lattices leads to particularly simple formulae. These sets were generalized by Lee and Phillips considering three-pencil lattices, generated by three linear pencils. Inspired by the addition of points on cubic curves and using duality, we introduce an addition of lines as a way of constructing lattices generated by cubic pencils. They include three-pencil lattices and then principal lattices. Interpolation on lattices generated by cubic pencils has the same good properties and simple formulae as on principal lattices.
24 citations
TL;DR: It is shown that the way in which the derivatives are approximated is crucial for the success of the method, and a new way to compute them is presented that makes the scheme adequate for non-smooth data.
24 citations
24 citations
TL;DR: This method provides not only a large variety of very interesting shape controls like biased, point, and interval tensions but, as a special case, also recovers the cubic B-spline curve and the rational cubic spline with tension of Gregory and Sarfraz.
24 citations