Please use this identifier to cite or link to this item: https://scholarbank.nus.edu.sg/handle/10635/103070
Title: Convergence of cascade algorithms associated with nonhomogeneous refinement equations
Authors: Jia, R.-Q. 
Jiang, Q. 
Shen, Z. 
Keywords: Cascade algorithms
Nonhomogeneous refinement equations
Issue Date: 2001
Citation: Jia, R.-Q.,Jiang, Q.,Shen, Z. (2001). Convergence of cascade algorithms associated with nonhomogeneous refinement equations. Proceedings of the American Mathematical Society 129 (2) : 415-427. ScholarBank@NUS Repository.
Abstract: This paper is devoted to a study of multivariate nonhomogeneous refinement equations of the form φ(x) = g(x) + ∑αεℤs α(α)φ(Mx - α), x ε ℝs, where φ = (φ1,. . . , φr)T is the unknown, g = (g1,. . . , gr)T is a given vector of functions on ℝs, M is an s × s dilation matrix, and a is a finitely supported refinement mask such that each α(α) is an r × r (complex) matrix. Let φ0 be an initial vector in (L2(ℝs))r. The corresponding cascade algorithm is given by φk= φ + ∑αεℤs α(α)φk-1(M · - α), k = 1,2, . . . . In this paper we give a complete characterization for the L2-convergence of the cascade algorithm in terms of the refinement mask a, the nonhomogeneous term g, and the initial vector of functions φ0. © 2000 American Mathematical Society.
Source Title: Proceedings of the American Mathematical Society
URI: http://scholarbank.nus.edu.sg/handle/10635/103070
ISSN: 00029939
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