TY - JOUR
T1 - Some Observations Regarding Interpolants in the Limit of Flat Radial Basis Functions
AU - Fornberg, B.
AU - Wright, G.
AU - Larsson, E.
PY - 2004/1
Y1 - 2004/1
N2 - Radial basis functions (RBFs) form a primary tool for multivariate interpolation. Some of the most commonly used radial functions feature a shape parameter, allowing them to vary from being nearly flat (ε small) to sharply peaked (ε large). The former limit can be particularly accurate when interpolating a smooth function based on scattered data. This study discusses theoretical and computational aspects of the ε → 0 limit, and includes the conjecture that Gaussian RBF interpolants will never diverge in this limit.
AB - Radial basis functions (RBFs) form a primary tool for multivariate interpolation. Some of the most commonly used radial functions feature a shape parameter, allowing them to vary from being nearly flat (ε small) to sharply peaked (ε large). The former limit can be particularly accurate when interpolating a smooth function based on scattered data. This study discusses theoretical and computational aspects of the ε → 0 limit, and includes the conjecture that Gaussian RBF interpolants will never diverge in this limit.
KW - Multivariate interpolation
KW - Radial basis functions (RBF)
UR - http://www.scopus.com/inward/record.url?scp=0942300715&partnerID=8YFLogxK
U2 - 10.1016/S0898-1221(04)90004-1
DO - 10.1016/S0898-1221(04)90004-1
M3 - Article
AN - SCOPUS:0942300715
SN - 0898-1221
VL - 47
SP - 37
EP - 55
JO - Computers and Mathematics with Applications
JF - Computers and Mathematics with Applications
IS - 1
ER -