engleski

On Interpolation by Hermite Tension Splines of Arbitrary Order

For a given partition $x_0<x_<ldots x_n$, a Hermite tension spline of order $2k$ is a function that on each subinterval $(x_i,x_{i+1}$ satisfies the differential equation $D^{2k-2}(D^2-p_i^2/h_i^2u-0$ ($h_i=x_{i+1}-x_i$ and $p_i$'s are nonnegative real constants) and the interpolatatory conditions $u^{(j)}(x_i)=f_i^j,j=0,ldotsk-1,i=0,ldots n$ for prescribed real values $f_i^j$. For $p_i=0$ a Hermite tesnion spline is a classical Hermite polynomial spline of order $2k$, whereas for $p_i ightarrowinfty$ we obtain a Hermite polynomial spline of order $2k-2$. We discuss a behavior of such an interpolant, bounds for interpolation error and its behavior in the limit case when $p_i ightarrowinfty$.

Interpolation; Splines; Asymptotic Expansions; Green's Functions

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