|
|||||
|
|
On the Mathematical Properties of Distributed Approximating Functionals |
|
| Authors: | Guowei Wei Haixiang Wang Donald J. Kouri Manos Papadakis Ioannis A. Kakadiaris David K. Hoffman |
| Affiliation: | (1) Department of Computational Science, National University of Singapore, Singapore, 129260;(2) Department of Chemistry and Department of Physics, University of Houston, Houston, TX 77204-5641, USA;(3) Department of Mathematics, University of Houston, Houston, TX 77204-3476, USA;(4) Department of Computer Science, University of Houston, Houston, TX 77204-3475, USA;(5) Department of Chemistry and Ames Lab, Iowa State University, Ames, IA 50011, USA |
| Abstract: | This work investigates some mathematical properties of the Distributed Approximating Functionals (DAFs). We prove that certain classes of DAFs yield Unity Approximations. Two distinct classes which serve as examples are the Hermite-DAFs and the Sinc-class DAFs. Detailed proofs are given. A wavelet generator is constructed using the Continuous Wavelet Transform with repect to the scale parameter. Taking the Gaussian function as the scaling function, a numerical experiment is carried out demonstrating the use of the resulting wavelet for edge detection. |
| Keywords: | Distributed Approximating Functionals (DAFs) wavelet generator Gaussian function |
| 本文献已被 SpringerLink 等数据库收录！ | |