Meshless cubature by Green's formula

Applied Mathematics and Computation

Volumn 183, Issue 2, 2006, Pages 1098-1107

  Sommariva, Alvise ^a   Vianello, Marco ^a  

^a UNIVERSITY OF PADOVA   (Italy)

Author keywords

Green's formula; Numerical integration; Polygons; Scattered data; Thin plate splines

Indexed keywords

GREEN'S FUNCTION; INTEGRAL EQUATIONS;

GREEN'S FORMULA; POLYGONS; SCATTERED DATA; THIN-PLATE SPLINES;

INTERPOLATION;

EID: 33845761052     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2006.05.211     Document Type: Article

References (17)

1. Apostol T.M. Calculus. second ed. vol. II (1969), Blaisdel
2. Beatson R.K., Light W.A., and Billings S. Fast solution of the radial basis function interpolation equations: domain decomposition methods. SIAM J. Sci. Comput. 22 (2000) 1717-1740
3. Bezhaev A.Yu. Cubature formulae on scattered meshes. Soviet J. Numer. Anal. Math. Model. 6 (1991) 95-106
4. Buhmann M.D. Radial basis functions. Acta Numer. 9 (2000) 1-38
5. Buhmann M.D. Radial Basis Functions: Theory and Implementation. Cambridge Monographs on Applied and Computational Mathematics vol. 12 (2003), Cambridge University Press
6. In: Cools R., and Laurie D. (Eds). Numerical evaluation of integrals. J. Comput. Appl. Math. 112 (1999) 1-2
7. Fornberg B., Driscoll T.A., Wright G., and Charles R. Observations on the behavior of radial basis function approximations near boundaries. Comput. Math. Appl. 43 (2002) 473-490
8. G. Green, An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism, Nottingham, 1828.
9. Iske A. Multiresolution Methods in Scattered Data Modelling. Lecture Notes in Computational Science and Engineering vol. 37 (2004), Springer
10. Levin D. Stable integration rules with scattered integration points. Numerical evaluation of integrals. J. Comput. Appl. Math. 112 (1999) 181-187
11. The MathWorks, MATLAB Documentation Set, 2006 version (available online at http://www.mathworks.com).
12. Schaback R. Error estimates and condition numbers for radial basis function interpolation. Adv. Comput. Math. 3 (1995) 251-264
13. Schaback R., and Wendland H. Kernel Techniques: From Machine Learning to Meshless Methods. Acta Numer. 15 (2006) 543-639
14. Sommariva A., and Vianello M. Numerical cubature on scattered data by radial basis functions. Computing 76 (2006) 295-310
15. A. Sommariva, and R. Womersley, Integration by RBF over the sphere (preprint UNSW AMR05/17, available online at http://www.maths.unsw.edu.au) submitted for publication.
16. Wendland H. Scattered Data Approximation. Cambridge Monographs on Applied and Computational Mathematics vol. 17 (2005), Cambridge University Press
17. Wolfram Research, Inc., The Wolfram Integrator, 2005 version (available online at http://integrals.wolfram.com).