Adaptive cross-approximation for surface reconstruction using radial basis functions

Journal of Engineering Mathematics

Volumn 62, Issue 2, 2008, Pages 149-160

  Grzhibovskis, Richards ^a   Bambach, Markus ^b   Rjasanow, Sergej ^a   Hirt, Gerhard ^b  

^a SAARLAND UNIVERSITY   (Germany)

^b RWTH AACHEN UNIVERSITY   (Germany)

Author keywords

Blockwise low rank approximation; Digitized surface; Meshless interpolation; Metal sheet thickness

Indexed keywords

ADHESIVE JOINTS; COMPUTER NETWORKS; FEEDFORWARD NEURAL NETWORKS; IMAGE SEGMENTATION; RADIAL BASIS FUNCTION NETWORKS;

BLOCKWISE LOW-RANK APPROXIMATION; DIGITIZED SURFACE; MESHLESS INTERPOLATION; METAL-SHEET THICKNESS; SURFACE INTERPOLATION;

MATRIX ALGEBRA;

EID: 50649093328     PISSN: 00220833     EISSN: 15732703     Source Type: Journal    
DOI: 10.1007/s10665-007-9197-8     Document Type: Article

References (29)

1. Hardy R (1990). Theory and applications of the multiquadric-biharmonic method. 20 years of discovery 1968-1988. Comput Math Appl 19(8-9):163-208
2. Bookstein FL (1989). Principal warps: Thin-plate splines and the decomposition of deformations. IEEE Trans Pattern Anal Mach Intell 11:567-585
3. Barrodale I, Kuwahara R, Poeckert R and Skea D (1993). Side-scan sonar image processing using thin plate splines and control point matching. Numer Algorithms 5(1-4):85-98
4. Flusser J (1992). An adaptive method for image registration. Pattern Recognition 25(1):45-54
5. Dyn N, Levin D and Rippa S (1986). Numerical procedures for surface fitting of scattered data by radial functions. SIAM J Sci Statist Comput 7(2):639-659
6. Appel A (1985). An efficient program for many-body simulation. SIAM J Sci Statist Comput 6(1):85-103
7. Barnes J and Hut P (1986). A hierarchical O(N log N) force-calculation algorithm. Nature 324(6096):446-449
8. Greengard L and Rokhlin V (1987). A fast algorithm for particle simulations. J Comput Phys 73(2):325-348
9. Greengard L (1988) The rapid evaluation of potential fields in particle systems. ACM Distinguished Dissertations, MIT Press, Cambridge, MA
10. Ying L, Biros G and Zorin D (2004). A kernel-independent adaptive fast multipole algorithm in two and three dimensions. J Comput Phys 196(2):591-626
11. Hackbusch W and Nowak ZP (1989). On the fast matrix multiplication in the boundary element method by panel clustering. Numer Math 54(4):463-491
12. Beatson RK, Newsam GN (1992) Fast evaluation of radial basis functions. I. Comput Math Appl 24(12):7-19. Advances in the theory and applications of radial basis functions.
13. Cherrie J, Beatson R, Newsam G (2002) Fast evaluation of radial basis functions: Methods for generalized multiquadrics in ℝ″. SIAM J Sci Comput 23(5):1549-1571 (electronic)
14. Potts D, Steidl G and Nieslony A (2004). Fast convolution with radial kernels at nonequispaced knots. Numer Math 98(2):329-351
15. Bebendorf M (2000). Approximation of boundary element matrices. Numer Math 86(4):565-589
16. Bebendorf M and Grzhibovskis R (2006). Accelerating Galerkin BEM for linear elasticity using adaptive cross approximation. Math Meth Appl Sci 29(14):1721-1747
17. Bebendorf M and Rjasanow S (2000). Matrix compression for the radiation heat transfer in exhaust pipes. In: Wendland, W, Sändig, A-M and Schiehlen, W (eds) Multifield Problems. State of the Art, pp 183-192. Springer, Berlin
18. Bebendorf M and Rjasanow S (2003). Adaptive low-rank approximation of collocation matrices. Computing 70:1-24
19. Micchelli CA (1986). Interpolation of scattered data: Distance matrices and conditionally positive definite functions. Constr Approx 2(1):11-22
20. Meinguet J (1979). Multivariate interpolation at arbitrary points made simple. Z Angew Math Phys 30(2):292-304
21. Beatson RK, Cherrie JB, Mouat CT (1999) Fast fitting of radial basis functions: Methods based on preconditioned GMRES iteration. Adv Comput Math 11(2-3):253-270. Radial basis functions and their applications
22. Rjasanow S, Steinbach O (2007) The fast solution of boundary integral equations, Mathematical and Analytical Techniques with Applications to Engineering. Springer-Verlag, Berlin (to appear)
23. Saad Y and Schultz MH (1986). GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J Sci Statist Comput 7(3):856-869
24. Schaback R (2002) Stability of radial basis function interpolants. In: Approximation theory, X (St. Louis, MO, 2001). Vanderbilt University Press, Innov Appl Math Nashville, pp 433-440
25. Franke R (1982). Scattered data interpolation: Tests of some methods. Math Comp 38(157):181-200
26. Wendland H (1997) Sobolev-type error estimates for interpolation by radial basis functions. In: Surface fitting and multiresolution methods (Chamonix-Mont-Blanc, 1996). Vanderbilt University Press, Nashville, pp 337-344
27. Wendland H (2002) Scattered data modelling by radial and related functions. Habilitation Thesis, Universität Göttingen, Gottingen
28. Bebendorf M (2005). Hierarchical LU decomposition-based preconditioners for BEM. Computing 74(3):225-247
29. Bebendorf M (2006) Approximate inverse preconditioning of finite element discretizations of elliptic operators with nonsmooth coefficients. SIAM J Matrix Anal Appl 27(4):909-929 (electronic)