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|Title:||Multidimensional interpolatory subdivision schemes|
Interpolatory subdivision schemes
|Citation:||Riemenschneider, S.D.,Shen, Z. (1997). Multidimensional interpolatory subdivision schemes. SIAM Journal on Numerical Analysis 34 (6) : 2357-2381. ScholarBank@NUS Repository.|
|Abstract:||This paper presents a general construction of multidimensional interpolatory subdivision schemes. In particular, we provide a concrete method for the construction of bivariate interpolatory subdivision schemes of increasing smoothness by finding an appropriate mask to convolve with the mask of a three-direction box spline Br,r,r of equal multiplicities. The resulting mask for the interpolatory subdivision exhibits all the symmetries of the three-direction box spline and with this increased symmetry comes increased smoothness. Several examples are computed (for r = 2, . . . , 8). Regularity criteria in terms of the refinement mask are establíshed and applied to the examples to estimate their smoothness.|
|Source Title:||SIAM Journal on Numerical Analysis|
|Appears in Collections:||Staff Publications|
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