Topic

# Spline interpolation

About: Spline interpolation is a research topic. Over the lifetime, 8924 publications have been published within this topic receiving 174795 citations.

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TL;DR: It is demonstrated that arbitrary accuracy can be achieved, independent of system size N, at a cost that scales as N log(N), which is comparable to that of a simple truncation method of 10 A or less.

Abstract: The previously developed particle mesh Ewald method is reformulated in terms of efficient B‐spline interpolation of the structure factors This reformulation allows a natural extension of the method to potentials of the form 1/rp with p≥1 Furthermore, efficient calculation of the virial tensor follows Use of B‐splines in place of Lagrange interpolation leads to analytic gradients as well as a significant improvement in the accuracy We demonstrate that arbitrary accuracy can be achieved, independent of system size N, at a cost that scales as N log(N) For biomolecular systems with many thousands of atoms this method permits the use of Ewald summation at a computational cost comparable to that of a simple truncation method of 10 A or less

15,288 citations

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TL;DR: It can be shown that the order of accuracy of the cubic convolution method is between that of linear interpolation and that of cubic splines.

Abstract: Cubic convolution interpolation is a new technique for resampling discrete data. It has a number of desirable features which make it useful for image processing. The technique can be performed efficiently on a digital computer. The cubic convolution interpolation function converges uniformly to the function being interpolated as the sampling increment approaches zero. With the appropriate boundary conditions and constraints on the interpolation kernel, it can be shown that the order of accuracy of the cubic convolution method is between that of linear interpolation and that of cubic splines. A one-dimensional interpolation function is derived in this paper. A separable extension of this algorithm to two dimensions is applied to image data.

2,789 citations

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01 Jan 1972

TL;DR: In this paper, a monograph describes and analyzes some practical methods for finding approximate zeros and minima of functions, and some of these methods can be used to find approximate minima as well.

Abstract: This monograph describes and analyzes some practical methods for finding approximate zeros and minima of functions.

2,471 citations

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TL;DR: In this paper, the authors generalize the results of [4] and modify the algorithm presented there to obtain a better rate of convergence, which is the same as in this paper.

Abstract: In this paper we generalize the results of [4] and modify the algorithm presented there to obtain a better rate of convergence.

2,163 citations

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TL;DR: In this article, a monotone piecewise bicubic interpolation algorithm was proposed for data on a rectangular mesh, where the first partial derivatives and first mixed partial derivatives are determined by the mesh points.

Abstract: In a 1980 paper [SIAM J. Numer. Anal., 17 (1980), pp. 238–246] the authors developed a univariate piecewise cubic interpolation algorithm which produces a monotone interpolant to monotone data. This paper is an extension of those results to monotone $\mathcal{C}^1 $ piecewise bicubic interpolation to data on a rectangular mesh. Such an interpolant is determined by the first partial derivatives and first mixed partial (twist) at the mesh points. Necessary and sufficient conditions on these derivatives are derived such that the resulting bicubic polynomial is monotone on a single rectangular element. These conditions are then simplified to a set of sufficient conditions for monotonicity. The latter are translated to a system of linear inequalities, which form the basis for a monotone piecewise bicubic interpolation algorithm.

1,942 citations