TY - JOUR
T1 - Computational aspects of approximation to scattered data by using 'shifted' thin-plate splines
AU - Yoon, Jungho
N1 - Funding Information:
I am grateful to Prof. Amos Ron for many helpful advices and suggestions which he offered during this work. This work was supported by Research Assistantships of Prof. Ron at University of Wisconsin-Madison (NSF Grant DMS-9626319 and the U.S. Army Research Office Contract DAAH04-95-1-0089). I would also like to express my appreciation to Prof. Carl de Boor for his help for the algorithm and numerical tests.
PY - 2001
Y1 - 2001
N2 - A new multivariate approximation scheme to scattered data on arbitrary bounded domains in ℝd is developed. The approximant is selected from a space spanned (essentially) by corresponding translates of the 'shifted' thin-plate spline ('essentially,' since the space is augmented by certain functions in order to eliminate boundary effects). This scheme applies to noisy data as well as to noiseless data, but its main advantage seems to be in the former case. We suggest an algorithm for the new approximation scheme with a detailed description (in a MATLAB-like program). Some numerical examples are presented along with comparisons with thin-plate spline interpolation and Wahba's thin-plate smoothing spline approximation.
AB - A new multivariate approximation scheme to scattered data on arbitrary bounded domains in ℝd is developed. The approximant is selected from a space spanned (essentially) by corresponding translates of the 'shifted' thin-plate spline ('essentially,' since the space is augmented by certain functions in order to eliminate boundary effects). This scheme applies to noisy data as well as to noiseless data, but its main advantage seems to be in the former case. We suggest an algorithm for the new approximation scheme with a detailed description (in a MATLAB-like program). Some numerical examples are presented along with comparisons with thin-plate spline interpolation and Wahba's thin-plate smoothing spline approximation.
KW - 'Shifted' thin-plate spline
KW - Approximation order
KW - Gauss elimination by degree
KW - Radial basis function
KW - Scattered data approximation
UR - http://www.scopus.com/inward/record.url?scp=0035623507&partnerID=8YFLogxK
U2 - 10.1023/A:1012205804632
DO - 10.1023/A:1012205804632
M3 - Article
AN - SCOPUS:0035623507
VL - 14
SP - 329
EP - 359
JO - Advances in Computational Mathematics
JF - Advances in Computational Mathematics
SN - 1019-7168
IS - 4
ER -