Lagrange interpolation for continuous piecewise smooth functions

A Modified Adaptive Quadrature Scheme for Continuous Piecewise-Smooth Functions

Approximating Piecewise-Smooth Functions

We consider the possibility of using locally supported quasi-interpolation operators for the approximation of univariate non-smooth functions. In such a case one usually expects the rate of approximation to be lower than that of smooth functions. It is shown in this paper that prior knowledge of the type of ’singularity’ of the function can be used to regain the full approximation power of the ...

Piecewise-smooth Refinable Functions

Univariate piecewise-smooth refinable functions (i.e., compactly supported solutions of the equation φ( 2 ) = ∑N k=0 ckφ(x−k)) are classified completely. Characterization of the structure of refinable splines leads to a simple convergence criterion for the subdivision schemes corresponding to such splines, and to explicit computation of the rate of convergence. This makes it possible to prove a...

ENO-Wavelet Transforms for Piecewise Smooth Functions

We have designed an adaptive essentially nonoscillatory (ENO)-wavelet transform for approximating discontinuous functions without oscillations near the discontinuities. Our approach is to apply the main idea from ENO schemes for numerical shock capturing to standard wavelet transforms. The crucial point is that the wavelet coefficients are computed without differencing function values across ju...

Some new results on Lagrange interpolation for bounded variation functions

The paper deals with the Lagrange interpolation of functions having a bounded variation derivative. For special systems of nodes, it is shown that this polynomial sequence converges with the best approximation order. The L weighted case is also discussed.