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: A study of different cubic interpolation kernels in the frequency domain is presented that reveals novel aspects of both cubic spline and cubic convolution interpolation.
Abstract: A study of different cubic interpolation kernels in the frequency domain is presented that reveals novel aspects of both cubic spline and cubic convolution interpolation. The kernel used in cubic convolution is of finite support and depends on a parameter to be chosen at will. At the Nyquist frequency, the spectrum attains a value that is independent of this parameter. Exactly the same value is found at the Nyquist frequency in the cubic spline interpolation. If a strictly positive interpolation kernel is of importance in applications, cubic convolution with the parameter value zero is recommended. >
267 citations
265 citations
TL;DR: The design of algorithms for interpolating discrete data using $C^1 $-quadratic splines in such a way that the monotonicity and/or convexity of the data is preserved is discussed.
Abstract: In this paper we discuss the design of algorithms for interpolating discrete data using $C^1 $-quadratic splines in such a way that the monotonicity and/or convexity of the data is preserved. The analysis culminates in an interactive algorithm which takes full advantage of the flexibility which quadratic splines permit.
255 citations
TL;DR: In this paper, a limit form of Richardson extrapolation is used to obtain interpolation formulae with accuracy of a higher degree than that obtained with the variation diminishing spline approximation.
244 citations
231 citations