Local Lagrange Interpolation with Bivariate Splines of Arbitrary Smoothness

Nürbberger, Günther; Rayevskaya, Vera; Schumaker, Larry L.; Zeilfelder, Frank
December 2005
Constructive Approximation;Nov2005, Vol. 23 Issue 1, p33
Academic Journal
We describe a method which can be used lo interpolate function values at a set ot scattered points in a planar domain using bivariate polynomial splines of any prescribed smoothness. The method starts with an arbitrary given triangulation of the data points, and involves refining sonic of the triangles with Clough-Tocher splits. The construction of the interpolating splines requires some additional function values at selected points in the domain, but no derivatives are needed at any point. Given n data points and a corresponding initial triangulation. the interpolating spline can be computed in just O(n) operations. The interpolation method is local and stable, and provides optimal order approximation of smooth functions,


Related Articles

  • Local Hermite Interpolation by Bivariate C¹ Cubic Splines on Checkerboard Triangulations. Sun-Kang Chen; Huan-Wen Liu; Xiang-Zhao Cui // Journal of Computational Analysis & Applications;Jan2012, Vol. 14 Issue 1, p559 

    Given a so-call checkerboard quadrangulation ◊̄, a checkerboard triangulation … can be obtained by adding two diagonals of all quadrilaterals in ◊̄. In this paper, we develop a local Hermite interpolation method for bivariate C¹ cubic splines on …. By enforcing...

  • A New Error Bound for Shifted Surface Spline Interpolation. Lin-Tian Luh // Studies in Mathematical Sciences;Nov2010, Vol. 1 Issue 1, p1 

    Shifted surface spline is a frequently used radial function for scattered data interpolation. The most frequently used error bounds for this radial function are the one raised by Wu and Schaback in [17] and the one raised by Madych and Nelson in [14]. Both are O(dl) as d → 0, where l is a...

  • Spline methods for a Birkhoff interpolation problem. Lang, Feng-Gong; Xu, Xiao-Ping // Calcolo;Sep2014, Vol. 51 Issue 3, p485 

    In this paper, we study two new spline methods for the Birkhoff interpolation problem proposed in Costabile and Longo (Calcolo 47:49-63, ). Our methods are based on cubic spline and quintic spline respectively. The new methods are easy to be implemented. They are effective not only in...

  • Application of Radial Point Interpolation Method to Temperature Field. Yu Chen; Maohui Xia; Dehua Wang; Dongmei Li // Journal of Mathematics Research;Feb2010, Vol. 2 Issue 1, p139 

    A point interpolation which bases on the radial function is a new meshless method. It is advantageous over the original PIM with polynomial basis in avoiding singularity when shape functions are constructed. It is also easy to deal with essential boundary for its property of Kronecher Delta...

  • Use of B-spline curves and genetic algorithms to reduce the sidelobe level in array-patterns. Wen-Chia Lue; Fang Hsu // Microwave & Optical Technology Letters;8/20/2003, Vol. 38 Issue 4, p308 

    A method of minimizing the sidelobe level for linear array patterns by amplitude-only adjustment in element excitations, which involves combining B-spline techniques and genetic algorithms, is considered. We demonstrate this technique using a 30-element linear array. It is also capable of...

  • Chordal cubic spline interpolation is fourth-order accurate. Floater, Michael S. // IMA Journal of Numerical Analysis;Jan2006, Vol. 26 Issue 1, p25 

    It is well known that complete cubic spline interpolation of functions with four continuous derivatives is fourth-order accurate. In this paper we show that this kind of interpolation, when used to construct parametric spline curves through sequences of points in any space dimension, is again...

  • Convexity preserving C splines. Schumaker, Larry; Speleers, Hendrik // Advances in Computational Mathematics;Feb2014, Vol. 40 Issue 1, p117 

    Linear conditions for a C spline to be convex are developed and used to create some convexity preserving interpolation and approximation methods.

  • Approximation of derivatives by jumps of interpolating splines. Volkov, Yu. S.; Miroshnichenko, V. L. // Mathematical Notes;Feb2011, Vol. 89 Issue 1/2, p138 

    The article examines the approximation of derivatives by means of jumps of interpolating splines. It investigates the interpolation values of a smooth mathematical function. It also analyzes linear equations, periodic analog, and mathematical theorem. It also shows that the theorem used in the...

  • Spline Interpolation on Unbounded Domains. Skeel, Robert D. // AIP Conference Proceedings;2016, Vol. 1738 Issue 1, p020001-1 

    Spline interpolation is a splendid tool for multiscale approximation on unbounded domains. In particular, it is well suited for use by the multilevel summation method (MSM) for calculating a sum of pairwise interactions for a large set of particles in linear time. Outlined here is an algorithm...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics