Convergence and error estimates for (m,l,s)-splines

Error Estimates and Convergence Rates for Filtered Back Projection

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 estimates and free-boundary convergence for a finite difference discretization of a parabolic variational inequality

— We study a free-boundary problem ofbiological interest, for the heat équation ; the problem is reduced to a variational inequality, which is solved by means ofafinite différence method. We aiso give an error estimaté, in the L^-norm, for the solution of the inequality, and a convergence theorem for the discrete free boundaries, The latter follows from a gênerai resuit concerning the behaviour...

Convergence and Error Estimates of Relaxation Schemes for Multidimensional Conservation Laws

M. A. Katsoulakis, G. Kossioris and Ch. Makridakis Abstract. We study discrete and semidiscrete relaxation schemes for multidimensional scalar conservation laws. We show convergence of the relaxation schemes to the entropy solution of the conservation law and derive error estimates that exhibit the precise interaction between the relaxation time and the space/time discretization parameters of t...