Estimates for spline projections

Estimates for spline projections

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Explicit localization estimates for spline-type spaces

holds for every c ∈ `, and the functions {fk}k satisfy an spatial localization condition. In a spline-type space any function in f ∈ S has a unique expansion f = ∑ k ckfk. Moreover the coefficients are given by ck = 〈f, gk〉, where {gk}k ⊆ S is the dual basis, a set of functions characterized by the relation 〈gk, fj〉 = δk,j . These spaces provide a very natural framework for the sampling problem...

Smoothing Spline Regression Estimates for Randomly Right Censored Data

Error Estimates for Thin Plate Spline Approximation in the Disc

This paper is concerned with approximation properties of linear combinations of scattered translates of the thin-plate spline radial basis function | · | log | · | where the translates are taken in the unit disc D in R. We show that the Lp approximation order for this kind of approximation is 2+1/p (for sufficiently smooth functions), which matches Johnson’s upper bound and, thus, gives the sat...

SPLINE COLLOCATION FOR NONLINEAR FREDHOLM INTEGRAL EQUATIONS

The collocation method based on cubic B-spline, is developed to approximate the solution of second kind nonlinear Fredholm integral equations. First of all, we collocate the solution by B-spline collocation method then the Newton-Cotes formula use to approximate the integrand. Convergence analysis has been investigated and proved that the quadrature rule is third order convergent. The presented...