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 -