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, a new Bayesian approach for monotone curve fitting based on the isotonic regression model is proposed, where the unknown linear regression function is approximated by a cubic spline and the constraints are represented by the intersection of quadratic cones.
Abstract: This article proposes a new Bayesian approach for monotone curve fitting based on the isotonic regression model. The unknown monotone regression function is approximated by a cubic spline and the constraints are represented by the intersection of quadratic cones. We treat the number and locations of knots as free parameters and use reversible jump Markov chain Monte Carlo to obtain posterior samples of knot configurations. Given the number and locations of the knots, second-order cone programming is used to estimate the remaining parameters. Simulation results suggest the method performs well and we illustrate the approach using the ASA car data.
14 citations
01 Jan 1971
13 citations
24 Jun 2010
TL;DR: An intuitive approach to designing spatial C2 Pythagorean---hodograph (PH) quintic spline curves, based on given control polygons, is presented.
Abstract: An intuitive approach to designing spatial C2 Pythagorean---hodograph (PH) quintic spline curves, based on given control polygons, is presented. Although PH curves can always be represented in Bezier or B---spline form, changes to their control polygons will usually compromise their PH nature. To circumvent this problem, an approach similar to that developed in [13] for the planar case is adopted. Namely, the "ordinary" C2 cubic B---spline curve determined by the given control polygon is first computed, and the C2 PH spline associated with that control polygon is defined so as to interpolate the nodal points of the cubic B---spline, with analogous end conditions. The construction of spatial PH spline curves is more challenging than the planar case, because of the residual degrees of freedom it entails. Two strategies for fixing these free parameters are presented, based on optimizing shape measures for the PH spline curves.
13 citations
13 citations
TL;DR: The natural cubic spline interpolation procedure is introduced in a discursive fashion for sampling of digitized electroencephalographic data and useful applications include compatibility among diverse hardware and software and the customization of data analysis.
Abstract: Resampling of digitized electroencephalographic data allows changing the sampling rate with minimal distortion of the signal. Useful applications of the procedure include compatibility among diverse hardware and software and the customization of data analysis. The natural cubic spline interpolation procedure is introduced in a discursive fashion. A formal presentation is provided in the appendix.
13 citations