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: The problem of the representation of power-free integers by integral polynomials appears to have been first considered by Nageil [8], who shewed in 1922 that an irreducible polynomial f(n) of degree r > 2 is Z-free (i.e. not divisible by an Z-th power other than 1) for infinitely many n provided / r as discussed by the authors.
Abstract: The problem of the representation of power-free integers by integral polynomials appears to have been first considered by Nageil [8], who shewed in 1922 that an irreducible polynomial f(n) of degree r > 2 is Z-free (i. e. not divisible by an Z-th power other than 1) for infinitely many n provided / ^ r. This work was subsequently refined and developed by a number of writers, among whom we may mention Ricci, Estermann, Atkinson and Lord Gherwell, and Erdös. Using a sieve method Ricci [9], for example, proved in 1933 that, if N (x) — N (/, /) be the number of positive integers n not exceeding with the property that f(n) be /-free, then the asymptotic formula
11 citations
01 Jan 2010
TL;DR: It is demonstrated that the trilinear interpolation on the BCC lattice is competitive to the linear box-spline interpolation in terms of both efficiency and image quality.
Abstract: In this paper, we thoroughly study a trilinear interpolation scheme previously proposed for the Body-Centered Cubic (BCC) lattice. We think that, up to now, this technique has not received the attention that it deserves. By a frequency-domain analysis we show that it can isotropically suppress those aliasing spectra that contribute most to the postaliasing effect. Furthermore, we present an efficient GPU implementation, which requires only six trilinear texture fetches per sample. Overall, we demonstrate that the trilinear interpolation on the BCC lattice is competitive to the linear box-spline interpolation in terms of both efficiency and image quality. As a generalization to higher-order reconstruction, we introduce DC-splines that are constructed by convolving a Discrete filter with a Continuous filter, and easy to adapt to the Face-Centered Cubic (FCC) lattice as well.
11 citations
TL;DR: In this article, the authors developed a new approach to the problem of real-time interpolation of digital signals using local cubic polynomial interpolative routines known as cubic spline functions.
Abstract: Deals with the development of a new approach to the problem of real-time interpolation of digital signals. Whereas the traditional methods of performing this operation make use of digital filters (FIR or IIR), this approach utilizes local cubic polynomial interpolative routines known as cubic spline functions. By using cubic splines, an algorithm has been obtained which can be implemented in a simple and economical way, yielding the desired real-time interpolator. The properties of this system include conceptual and structural simplicity, local control, speed of operation, and versatility.
11 citations
TL;DR: In this article, a wide class of sufficient conditions that admit a G1 cubic spline interpolant is determined, and the existence requirements are based upon geometric properties of data entirely, and can be easily verified in advance.
Abstract: In this paper, geometric interpolation by G1 cubic spline is studied. A wide class of sufficient conditions that admit a G1 cubic spline interpolant is determined. In particular, convex data as well as data with inflection points are included. The existence requirements are based upon geometric properties of data entirely, and can be easily verified in advance. The algorithm that carries out the verification is added.
11 citations
TL;DR: In this article, the singularly perturbed boundary value problem for a second order delay differential equation is solved by a difference scheme based on cubic spline in tension, which converges to the continuous solution uniformly with respect to the perturbation parameter.
Abstract: This paper deals with the singularly perturbed boundary value problem for a second order delay differential equation. Similar boundary value problems are associated with expected first-exit times of the membrane potential in models of neurons. A difference scheme on a uniform mesh is accomplished by the method based on cubic spline in tension. The difference scheme is shown to converge to the continuous solution uniformly with respect to the perturbation parameter, which is illustrated with numerical results.
11 citations