TITLE

FUNDAMENTAL SOLUTIONS OF PDES AS RADIAL BASIS FUNCTIONS IN MULTIVARIATE INTERPOLATION

AUTHOR(S)
Masjukov, A.
PUB. DATE
October 2007
SOURCE
Computational Methods in Applied Mathematics;2007, Vol. 7 Issue 4, p321
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
For bivariate and trivariate interpolation we propose in this paper a set of integrable radial basis functions (RBFs). These RBFs are found as fundamental solutions of appropriate PDEs and they are optimal in a special sense. The condition number of the interpolation matrices as well as the order of convergence of the interpolation are estimated. Moreover, the proposed RBFs provide smooth approximations and approximate fulfillment of the interpolation conditions. This property allows us to avoid the undecidable problem of choosing the right scale parameter for the RBFs. Instead we propose an iterative procedure in which a sequence of improving approximations is obtained by means of a decreasing sequence of scale parameters in an a priori given range. The paper provides a few clear examples of the advantage of the proposed interpolation method.
ACCESSION #
28349899

 

Related Articles

  • A note on radial basis function interpolant limits. BUHMANN, MARTIN D.; DINEW, SŁAWOMIR; LARSSON, ELISABETH // IMA Journal of Numerical Analysis;Apr2010, Vol. 30 Issue 2, p543 

    Radial basis functions (RBFs) are very useful in multivariate interpolation because of their ability to produce highly accurate results for scattered data. Many of them, especially the Gaussian RBF and the multiquadric RBF, contain parameters that need to be adjusted in order to improve the...

  • A linearly conforming radial point interpolation method (LC-RPIM) for shells. Zhao, X.; Liu, G. R.; Dai, K. Y.; Zhong, Z. H.; Li, G. Y.; Han, X. // Computational Mechanics;Feb2009, Vol. 43 Issue 3, p403 

    In this paper, a linearly conforming radial point interpolation method (LC-RPIM) is presented for the linear analysis of shells. The first order shear deformation shell theory is adopted, and the radial and polynomial basis functions are employed to construct the shape functions. A strain...

  • APPROXIMATE IMPLICITIZATION BASED ON RBF NETWORKS AND MQ QUASI-INTERPOLATION. Renhong Wang; Jinming Wu // Journal of Computational Mathematics;Jan2007, Vol. 25 Issue 1, p97 

    In this paper, we propose a new approach to solve the approximate implicitization problem based on RBF networks and MQ quasi-interpolation. This approach possesses the advantages of shape preserving, better smoothness, good approximation behavior and relatively less data etc. Several numerical...

  • Positive Approximation and Interpolation Using Compactly Supported Radial Basis Functions. Jinming Wu; Xiaolei Zhang; Lihui Peng // Mathematical Problems in Engineering;2010, Vol. 2010, Special section p1 

    We discuss the problem of constrained approximation and interpolation of scattered data by using compactly supported radial basis functions, subjected to the constraint of preserving positivity. The approaches are presented to compute positive approximation and interpolation by solving the two...

  • Direct form seminorms arising in the theory of interpolation by Hankel translates of a basis function. Arteaga, Cristian; Marrero, Isabel // Advances in Computational Mathematics;Feb2014, Vol. 40 Issue 1, p167 

    Certain spaces of functions which arise in the process of interpolation by Hankel translates of a basis function, as developed by the authors elsewhere, are defined with respect to a seminorm which is given in terms of the Hankel transform of each function. This kind of seminorm is called an...

  • Stabilizing of Subspaces Based on DPGA and Chaos Genetic Algorithm for Optimizing State Feedback Controller. Hosseinpour, M.; Nikdel, P.; Badamchizadeh, M. A.; Poor, M. A. // Mathematical Problems in Engineering;2012, Vol. 2012, Special section p1 

    The main purpose of the paper is to optimize state feedback parameters using intelligent method, GA, Hermite-Biehler, and chaos algorithm. GA is implemented for local search but it has some deficiencies such as trapping into a local minimum and slow convergence, so the combination of...

  • Numerical Solution of Solid Mechanics Problems Using a Boundary-Only and Truly Meshless Method. Xiaolin Li // Mathematical Problems in Engineering;2012, Vol. 2012, Special section p1 

    Combining the hybrid displacement variational formulation and the radial basis point interpolation, a truly meshless and boundary-only method is developed in this paper for the numerical solution of solid mechanics problems in two and three dimensions. In this method, boundary conditions can be...

  • Multivariate Interpolation by Polynomials and Radial Basis Functions. Schaback, Robert // Constructive Approximation;2005, Vol. 21 Issue 3, p293 

    In many cases, multivariate interpolation by smooth radial basis functions converges toward polynomial interpolants, when the basis functions are scaled to become flat. In particular, examples show and this paper proves that interpolation by scaled Gaussians converges toward the de Boor/Ron...

  • Analysis of Compactly Supported Transformations for Landmark-based Image Registration. Cavoretto, Roberto; De Rossi, Alessandra // Applied Mathematics & Information Sciences;2013, Vol. 7 Issue 6, p2113 

    In this paper we consider landmark-based image registration using radial basis function interpolation schemes. More precisely, we analyze some landmark-based image transformations using compactly supported radial basis functions such as Wendland's, Wu's, and Gneiting's functions. Comparisons of...

Share

Read the Article

Courtesy of THE LIBRARY OF VIRGINIA

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

Try another library?
Sign out of this library

Other Topics