### Error Estimate of a Subdivision Scheme with a Truncated Refinement Mask

### Bin Han

## Abstract

Given a finitely supported refinement mask on $\bZ^s$ with
irrational coefficients,
in many applications, we need to truncate the irrational coefficients in
the refinement mask to rational numbers. This note provides a sharp error
estimate in the $L_p\, (1\le p \le \infty)$ norm sense of a multivariate
subdivision scheme caused by truncation of an original refinement mask.
Examples are provided to illustrate that the estimate in this note is optimal.
Finally, we partially extend this estimate to the case when a refinement
mask has infinite support.

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