Polynomial Reproduction in Subdivision

Abstract. We study conditions on the matrix mask of a vector subdivision scheme ensuring that certain polynomial input vectors yield polynomial output again. The conditions are in terms of a recurrence formula for the vectors which determine the structure of polynomial input with this property. From this recurrence, we obtain an algorithm to determine polynomial input of maximal degree. The algorithm can be used in the design of masks to achieve a high order of polynomial reproduction. Keywords. Vector subdivision, polynomial reproduction. 1991 Mathematics Subject Classification. 41A15, 65D17, 68U07.

• Type: Journal
• Year: 2004
• Where: ADCM
• Authors: Kurt Jetter, G. Zimmermann
• Keywords: ADCM 2004, Polynomial Input, Polynomial Input Vectors, Vector Subdivision