Showing papers by "Yuesheng Xu published in 1994"
TL;DR: In this article, the authors construct discontinuous wavelets on invariant sets in R n by using the matrix refinement equation and the basic operation of translation and scale, and show how to modify their construction to obtain continuous wavelets.
121 citations
TL;DR: In this article, the Gauss-type quadrature formulas for weakly singular integrals were established and applied to obtain numerical solutions of the second-order Fredholm integral equation.
Abstract: In this paper we establish Gauss-type quadrature formulas for weakly singular integrals. An application of the quadrature scheme is given to obtain numerical solutions of the weakly singular Fredholm integral equation of the second kind. We call this method a discrete product-integration method since the weights involved in the standard product-integration method are computed numerically.
106 citations
34 citations
02 Dec 1994
TL;DR: A procedure to recursively generate orthonormal bases with any prescribed number of continuous derivatives with applicability to smooth wavelets with and without boundary conditions is described.
Abstract: This paper continues the work in [4] on constructing orthogonal bases on the interval [0,1] by using the matrix refinement equation and the two basic operations of translation and scale. We call the elements of these bases wavelets. Here we amplify on the applicability of our method and construct smooth wavelets with and without boundary conditions. That is, we describe a procedure to recursively generate orthonormal bases with any prescribed number of continuous derivatives. As a caveat to the reader we reiterate our remark above that this paper is a continuation of our work in [4] and therefore some familiarity with [4] is assumed.
8 citations