Monotonicity Preserving Interpolatory Subdivision Schemes

摘要

A class of local nonlinear stationary subdivision schemes that interpolate211u001euniform data and that preserve monotonicity in the data is examined. The limit 211u001efunction obtained after repeated application of these schemes exists and is 211u001emonotone for arbitrary monotone initial data. Next a class of rational 211u001esubdivision schemes is examined. These schemes generate limit functions that are 211u001econtinuously differentiable for any strictly monotone data. The approximation 211u001eorder of the schemes is four. Some generalizations, such as preservation of 211u001epiecewise monotonicity and application to homogeneous grid refinement, are 211u001ebriefly discussed.