On the smoothness of real-valued functions generated by subdivision schemes using nonlinear binary averaging Academic Article uri icon

abstract

  • Our main result is that two point interpolatory subdivision schemes using Ck nonlinear averaging rules on pairs of real numbers generate real-valued functions that are also Ck. The significance of this result is the following consequence: Suppose that S is a subdivision algorithm operating on sequences of real numbers using linear binary averaging that generates Cm real-valued functions and over(S, -) is the same subdivision procedure where linear binary averaging is replaced everywhere in the algorithm by a Cn nonlinear binary averaging rule on pairs of real numbers; then the functions generated by the nonlinear subdivision scheme over(S, -) are Ck, where k = min (m, n). © 2008 Elsevier B.V. All rights reserved.

author list (cited authors)

  • Goldman, R., Vouga, E., & Schaefer, S.

citation count

  • 3

publication date

  • February 2009