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: This letter proposes a frequency-domain weighted least-squares (WLS) method for designing a length-6 cubic interpolation kernel constructed by connecting three piecewise polynomials of third-degree, and the optimal coefficients are found through minimizing the weighted squared error between the desired and actual frequency responses of the length- 6 cubic.
Abstract: This letter proposes a frequency-domain weighted least-squares (WLS) method for designing a length-6 cubic interpolation kernel constructed by connecting three piecewise polynomials of third-degree, and the optimal coefficients are found through minimizing the weighted squared error between the desired and actual frequency responses of the length-6 cubic. This frequency-domain approach can design various cubics with different frequency responses by adjusting the weighting functions in different frequency bands, and even ignore “don't care” bands. An interpolation example is given to illustrate that the length-6 cubic can achieve much higher accuracy interpolations than the other interpolators with fixed frequency characteristics.
4 citations
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TL;DR: This article describes how a transformation in parameter space relates to the transformation in coefficient space and wants to get insight into how cubic polynomials work, what are the invariants/covariants and their geometric interpretations.
Abstract: For pt.2 see ibid., vol. 26, no. 4, p. 90-100 (2006). Our ultimate goal here is twofold. We want to get insight into how cubic polynomials work, what are the invariants/covariants and their geometric interpretations. This article also describes how a transformation in parameter space relates to the transformation in coefficient space
4 citations
01 Jan 2012
TL;DR: In this article, a piecewise rational cubic function was developed to preserve the shape of monotonic data, which has two free parameters in its description, and the error bound was established as O( 3 h ).
Abstract: A piecewise rational cubic function is developed to preserve the shape of monotonic data. The rational cubic function has two free parameters in its description. Rational cubic functions are extended to rational bicubic partially blended functions. Simple data dependent constraints are derived on free parameters in the description of rational functions to conserve the shape of monotone 2D and 3D data. The developed schemes have unique representation. The error bounds of the piecewise rational cubic function is established as O( 3 h ).
4 citations
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TL;DR: In this paper, four types of numerical methods namely: Natural Cubic Spline, Special A-D cubic spline, FTCS and Crank-Nicolson are applied to both advection and diffusion terms of the one-dimensional adveection-diffusion equations with constant coefficients.
Abstract: Four types of numerical methods namely: Natural Cubic Spline, Special A-D Cubic Spline, FTCS and Crank–Nicolson are applied to both advection and diffusion terms of the one-dimensional advection-diffusion equations with constant coefficients. The numerical results from two examples are tested with the known analytical solution. The errors are compared when using different Peclet numbers.
4 citations
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4 citations