Error bounds for two even degree tridiagonal splines

Best Error Bounds for Splines of Degree Six

In this paper, we construct a spline method for solving a interpolation problem using piecewise polynomial of degree six which agree with the given function and its derivative at knots and the function at mid points also. Best error bounds are estimated.

Uniform Error Bounds for Smoothing Splines

Almost sure bounds are established for the uniform error of smoothing splines in nonparametric regression with random designs. Some kernel-like properties of the Green’s function for an appropriate boundary value problem are needed to reduce the problem to that for kernel-like regression estimators. Then, results of Einmahl and Mason (2005) imply the required bounds, uniformly in the smoothing ...

Uniform error bounds for smoothing splines

Almost sure bounds are established on the uniform error of smoothing spline estimators in nonparametric regression with random designs. Some results of Einmahl and Mason (2005) are used to derive uniform error bounds for the approximation of the spline smoother by an “equivalent” reproducing kernel regression estimator, as well as for proving uniform error bounds on the reproducing kernel regre...

Error Bounds for Minimal Energy Interpolatory Spherical Splines

The convergence of the minimal energy interpolatory splines on the unit sphere is studied in this paper. An upper bound on the difference between a sufficiently smooth function and its interpolatory spherical spline in the infinity norm is given. The error bound is expressed in terms of a second order spherical Sobolev-type seminorm of the original function. §

Error bounds for minimal energy bivariate polynomial splines