How is a Vector Pyramid Scheme Affected by Perturbation in the Mask?

Bin Han and Thomas A. Hogan


When implementing a pyramid scheme on a computer, it is not possible to use the exact values of the terms of the refinement mask if some are irrational. The irrational terms must be perturbed. When this is the case, it is important to know that the pyramid scheme associated with the perturbed mask converges and that the limit function is close to the solution of the original refinement equation. In this paper, we provide sharp $L_p$ ($1\le p \le\infty$) error estimates for univariate vector pyramid schemes when the terms of a finitely supported mask are perturbed slightly.

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