TY - JOUR
T1 - Numerical differentiation by radial basis functions approximation
AU - Wei, T.
AU - Hon, Y. C.
PY - 2007/10
Y1 - 2007/10
N2 - Based on radial basis functions approximation, we develop in this paper a new com-putational algorithm for numerical differentiation. Under an a priori and an a posteriori choice rules for the regularization parameter, we also give a proof on the convergence error estimate in reconstructing the unknown partial derivatives from scattered noisy data in multi-dimension. Numerical examples verify that the proposed regularization strategy with the a posteriori choice rule is effective and stable to solve the numerical differential problem. © 2006 Springer Science+Business Media, Inc.
AB - Based on radial basis functions approximation, we develop in this paper a new com-putational algorithm for numerical differentiation. Under an a priori and an a posteriori choice rules for the regularization parameter, we also give a proof on the convergence error estimate in reconstructing the unknown partial derivatives from scattered noisy data in multi-dimension. Numerical examples verify that the proposed regularization strategy with the a posteriori choice rule is effective and stable to solve the numerical differential problem. © 2006 Springer Science+Business Media, Inc.
KW - numerical differentiation
KW - radial basis functions
KW - Tikhonov regularization
UR - http://www.scopus.com/inward/record.url?scp=34548265741&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-34548265741&origin=recordpage
U2 - 10.1007/s10444-005-9001-0
DO - 10.1007/s10444-005-9001-0
M3 - RGC 21 - Publication in refereed journal
SN - 1019-7168
VL - 27
SP - 247
EP - 272
JO - Advances in Computational Mathematics
JF - Advances in Computational Mathematics
IS - 3
ER -