CONVERGENCE FOR A CLASS OF CASCADE ALGORITHMS WITH NONNEGATIVE MASKS

CONVERGENCE FOR A CLASS OF CASCADE ALGORITHMS WITH NONNEGATIVE MASKS | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 26 July 2025 V1 Latest version Share on CONVERGENCE FOR A CLASS OF CASCADE ALGORITHMS WITH NONNEGATIVE MASKS Authors : LI CHENG 0009-0006-2148-5889 , XUFA FANG [email protected] , XUEYAN XIANG , and ZHIGANG YAO Authors Info & Affiliations https://doi.org/10.22541/au.175353678.87744040/v1 169 views 117 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract A refinement equation, which can be expressed as a functional equation of the form φ ( x ) = ∑ j ∈ Z a ( j ) φ ( m x − j ), x ∈ R, where φ is the unknown function defined on R, { a ( j )| j ∈Z} is a finitely supported sequence (called the refinement mask), and m> 1 is an integer dilation factor. Solutions to such equations, known as refinable functions, play crucial roles in spline theory, interpolation schemes for curve construction, wavelet analysis with compactly supported bases, fractal generation, and probability theory. In this paper, we show the minimum cardinality of the support of the nonnegative mask for a univariate cascade algorithm, which ensures the convergence of the corresponding algorithm. Supplementary Material File (convergence for a class of cascade algorithm.pdf) Download 288.71 KB Information & Authors Information Version history V1 Version 1 26 July 2025 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords convergence nonnegative mask univariate cascade algorithm Authors Affiliations LI CHENG 0009-0006-2148-5889 Lishui University View all articles by this author XUFA FANG [email protected] Lishui University View all articles by this author XUEYAN XIANG Lishui University View all articles by this author ZHIGANG YAO Lishui University View all articles by this author Metrics & Citations Metrics Article Usage 169 views 117 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation LI CHENG, XUFA FANG, XUEYAN XIANG, et al. CONVERGENCE FOR A CLASS OF CASCADE ALGORITHMS WITH NONNEGATIVE MASKS. Authorea . 26 July 2025. DOI: https://doi.org/10.22541/au.175353678.87744040/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu . 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