Orthonormal compactly supported wavelets with optimal Sobolev regularity: Numerical results

Numerical optimization is used to construct new orthonormal compactly supported wavelets with a Sobolev regularity exponent as high as possible among those mother wavelets with a fixed support length and a Axed number of vanishing moments. The increased regularity is obtained by optimizing the locations of the roots the scaling Filter has on the interval (/2, rr). The results improve those obtained by I. Daubechies (1988, Comm. Pure Appl. Math. 41, 909-996), H. Volkmer (1995, SIAM J. Math. Anal. 26, 1075-1087), and P. G. Lemarie-Rieusset and E. Zahrouni (1998, Appl. Comput. Harmon. Anal. 5, 92-105). (C) 2001 Academic Press.