TY - JOUR
T1 - Approximation properties of Sobolev splines and the construction of compactly supported equivalents
AU - Ward, John P
AU - Unser, Michael
PY - 2014/1/1
Y1 - 2014/1/1
N2 - In this paper, we construct compactly supported radial basis functions that satisfy optimal approximation properties. Error estimates are determined by relating these basis functions to the class of Sobolev splines. Furthermore, we derive new rates for approximation by linear combinations of nonuniform translates of the Sobolev splines. Our results extend previous work as we obtain rates for basis functions of noninteger order, and we address approximation with respect to the L∞ norm. We also use bandlimited approximation to determine rates for target functions with lower order smoothness.
AB - In this paper, we construct compactly supported radial basis functions that satisfy optimal approximation properties. Error estimates are determined by relating these basis functions to the class of Sobolev splines. Furthermore, we derive new rates for approximation by linear combinations of nonuniform translates of the Sobolev splines. Our results extend previous work as we obtain rates for basis functions of noninteger order, and we address approximation with respect to the L∞ norm. We also use bandlimited approximation to determine rates for target functions with lower order smoothness.
KW - Bandlimited approximation
KW - Error estimates
KW - Radial basis functions
UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84987653286&origin=inward
UR - https://www.scopus.com/inward/citedby.uri?partnerID=HzOxMe3b&scp=84987653286&origin=inward
U2 - 10.1137/130924615
DO - 10.1137/130924615
M3 - Article
SN - 0036-1410
VL - 46
SP - 1843
EP - 1858
JO - SIAM Journal on Mathematical Analysis
JF - SIAM Journal on Mathematical Analysis
IS - 3
ER -