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, a class of end conditions is derived for cubic spline functions by use of integration, and these end conditions are given in terms of function values at the knots (data), and give rise to O(h^4) spline approximation.
7 citations
01 Apr 1962
TL;DR: In this article, it was shown that a cubic form in n variables with rational coefficients always represents zero if n > 32, and this condition was later relaxed to n ≥ 29.
Abstract: It was proved by Davenport (2) that a cubic form in n variables with rational coefficients always represents zero if n > 32; and this condition was later (3) relaxed to n ≥ 29. The object of the present paper is to establish conditions under which a cubic form will represent every rational number other than zero, for rational values of the variables. The main result is as follows.
7 citations
18 Nov 2004
TL;DR: The experimental result reveals that with a comparable computational complexity, the truncated raised cosine interpolator is superior to the widely used interpolator with Keys cubic function.
Abstract: In this work, an interpolation filter using truncated raised cosine pulses for image resizing, is investigated. The rectangular-truncated raised cosine pulse with rolloff factor /spl beta//spl ges/0.5 and truncation length T/spl ges/4T/sub s/ is shown to be a good choice for interpolation. The experimental result reveals that with a comparable computational complexity, the truncated raised cosine interpolator is superior to the widely used interpolator with Keys cubic function. The result also reveals that the performance of the truncated raised cosine interpolator is only slightly worse than that of the least-square cubic B-spline interpolator, but with much lower computational or hardware complexity.
7 citations
7 citations
TL;DR: In the case of uniform grids, the error of the spline interpolant of a function defined on R has been well estimated as mentioned in this paper, and the difference between the interpolant and the quasi-interpolants has been estimated.
Abstract: In the case of uniform grids, the error of the spline interpolant of a function defined on R has been well estimated On the basis of the spline interpolation formula for functions defined on R we derive quasi‐interpolation formulae for functions defined on R or in a vicinity of a bounded interval, say [0,1], and we estimate the difference between the interpolant and the quasi‐interpolants
7 citations