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Scattered Date Interpolation from Principal Shift-Invariant Spaces

โœ Scribed by Michael J Johnson

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
171 KB
Volume
113
Category
Article
ISSN
0021-9045

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โœฆ Synopsis

Under certain assumptions on the compactly supported function f ยฅ C(R d ), we propose two methods of selecting a function s from the scaled principal shiftinvariant space S h (f) such that s interpolates a given function f at a scattered set of data locations. For both methods, the selection scheme amounts to solving a quadratic programming problem and we are able to prove error estimates similar to those obtained by Duchon for surface spline interpolation.

๐Ÿ“œ SIMILAR VOLUMES

Quasi-Interpolation in Shift Invariant S
Quasi-Interpolation in Shift Invariant Spaces
โœ H.N. Mhaskar; F.J. Narcowich; J.D. Ward ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 83 KB

Let s โ‰ฅ 1 be an integer, ฯ† s โ†’ be a compactly supported function, and S ฯ† denote the linear span of ฯ† โ€ข -k k โˆˆ s . We consider the problem of approximating a continuous function f s โ†’ on compact subsets of s from the classes S ฯ† hโ€ข , h > 0, based on samples of the function at scattered sites in s .