Ehud Altman, Kenneth R. Brown, et al.
PRX Quantum
We introduce the concept of a refinable set relative to a family of contractive mappings on a metric space, and demonstrate how such sets are useful to recursively construct interpolants which have a multiscale structure. The notion of a refinable set parallels that of a refinable function, which is the basis of wavelet construction. The interpolation points we recursively generate from a refinable set by a set-theoretic multiresolution are analogous to multiresolution for functions used in wavelet construction. We then use this recursive structure for the points to construct multiscale interpolants. Several concrete examples of refinable sets which can be used for generating interpolatory wavelets are included.
Ehud Altman, Kenneth R. Brown, et al.
PRX Quantum
David L. Shealy, John A. Hoffnagle
SPIE Optical Engineering + Applications 2007
Chai Wah Wu
Linear Algebra and Its Applications
A. Gupta, R. Gross, et al.
SPIE Advances in Semiconductors and Superconductors 1990