TY - JOUR
AU1 - Bozzini, M.
AU2 - Lenarduzzi, L.
AU3 - Schaback, R.
AB - This paper applies difference operators to conditionally positive definite kernels in order to generate kernel

$$B$$
-splines that have fast decay towards infinity. Interpolation by these new kernels provides better condition of the linear system, while the kernel 
$$B$$
-spline inherits the approximation orders from its native kernel. We proceed in two different ways: either the kernel 
$$B$$
-spline is constructed adaptively on the data knot set 
$$X$$
, or we use a fixed difference scheme and shift its associated kernel 
$$B$$
-spline around. In the latter case, the kernel 
$$B$$
-spline so obtained is strictly positive in general. Furthermore, special kernel 
$$B$$
-splines obtained by hexagonal second finite differences of multiquadrics are studied in more detail. We give suggestions in order to get a consistent improvement of the condition of the interpolation matrix in applications.
TI - Kernel B-splines and interpolation
JF - Numerical Algorithms
DO - 10.1007/s11075-005-9000-8
DA - 2006-01-03
UR - https://www.deepdyve.com/lp/springer-journals/kernel-b-splines-and-interpolation-FwPSmkViaP
SP - 1
EP - 16
VL - 41
IS - 1
DP - DeepDyve
ER -