6533b7dbfe1ef96bd12713e2

RESEARCH PRODUCT

Proving convexity preserving properties of interpolatory subdivision schemes through reconstruction operators

Rosa DonatJuan Carlos TrilloSergio Amat

subject

AlgebraDiscrete mathematicsComputational MathematicsOperator (computer programming)Relation (database)business.industryHermite interpolationApplied MathematicsbusinessConvexityMathematicsSubdivision

description

We introduce a new approach towards proving convexity preserving properties for interpolatory subdivision schemes. Our approach is based on the relation between subdivision schemes and prediction operators within Harten's framework for multiresolution, and hinges on certain convexity properties of the reconstruction operator associated to prediction. Our results allow us to recover certain known results [10,8,1,7]. In addition, we are able to determine the necessary conditions for convexity preservation of the family of subdivision schemes based on the Hermite interpolation considered in [4].

yearjournalcountryeditionlanguage
2013-03-01Applied Mathematics and Computation
https://doi.org/10.1016/j.amc.2013.01.024