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 spline approximation for the gravitational field is obtained by using a Hilbert space with topology induced by the (Laplace-) Beltrami operator of the sphere, and the method is demonstrated for a spherical earth model.
Abstract: The mathematical framework for a spline method combining interpolation and smoothing of heterogeneous data is presented. The method is demonstrated for a spherical earth model. A spline approximation for the gravitational field is obtained by using a Hilbert space with topology induced by the (Laplace-) Beltrami operator of the sphere.
20 citations
01 Jan 2006
TL;DR: In this paper, an alternative method to the method proposed in (10) for the numerical eval- uation of integrals of the form R 1 i 1 e it f (t)dt, where f(t) has a simple pole in (i1;1) and R 2 R may be large, has been developed.
Abstract: An alternative method to the method proposed in (10) for the numerical eval- uation of integrals of the form R 1 i1 e it f(t)dt, where f(t) has a simple pole in (i1;1) and ` 2 R may be large, has been developed. The method is based on a special case of Hermite interpolation polynomial and it is comparatively simpler and entails fewer function evalua- tions and thus faster, but the two methods are comparable in accuracy. The validity of the method is demonstrated in the provision of two numerical experiments and their results.
20 citations
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TL;DR: The purpose of the procedures presented here is to determine the interpolating quintic natural spline function S ( x ) for the set of data points (x, ,y.), i = N 1, N I ~ I , . . . , N2, where it is assumed tha t x ~ < x~+~ < • • • < xN2 •
Abstract: The purpose of the procedures presented here is to determine the interpolating quintic natural spline function S ( x ) for the set of data points (x, ,y.) , i = N 1 , N I ~ I , . . . , N2, where it is assumed tha t x ~ < x~+~ < • • • < xN2 • The interpolating quintic natural spline function S ( x ) with the knots x ~ , . . . , XN2 has the following properties: (i) S ( x ) is a polynomial of degree 5 in each interval (x,, x,+~), i = N 1 , . . . , N 2 1 . (ii) S ( x ) and its derivatives S ' ( x ) , S\" (x), S \" ( x ) , and S \" ( x ) are continuous in [x~l.x~2]. (iii) S \" (X~l) = S \" (x~2) = S \" (x~l) = S \" (XN2) = O. (iv) S(x , ) = y,, i = N 1 , . . . , N2. I t is known tha t if N2 > N l k l , then there is a unique quintic natural spline function which has the properties ( i ) ( i v ) . (See, for example, Greville [3, 4].) This spline function can be represented in the form
20 citations
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TL;DR: In this paper, the spatial domain is divided into fixed subdomains and the number of collocation points for each subdomain is adaptively adjusted according to the present location and advancement speed of the maximum gradient.
20 citations
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TL;DR: Based on a cross-zonal filter in the two-dimensional cubic-spline interpolation and a symmetric extension method, an efficient algorithm is proposed for image coding that yields a better quality of reconstructed image than other interpolation methods.
Abstract: Based on a cross-zonal filter in the two-dimensional (2-D) cubic-spline interpolation (CSI) and a symmetric extension method, an efficient algorithm is proposed for image coding. Experimental results show that the proposed method is superior in performance and yields a better quality of reconstructed image than other interpolation methods.
20 citations