{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:29:14Z","timestamp":1787336954093,"version":"build-2736575974"},"reference-count":19,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Matrix Anal. Appl."],"published-print":{"date-parts":[[2003,1]]},"abstract":"<jats:p>In this paper, a parameterization is developed of orthogonal multiwavelets that have all scaling and wavelet functions symmetric or antisymmetric about some given point. The parameterization is based on the factorization of the polyphase matrix into the product of an orthogonal matrix and paraunitary linear factors based on complementary orthogonal projectors. The symmetry of scaling and wavelet functions is reflected by the polyphase matrix. It can be enforced by using factors that themselves conform to certain symmetry constraints. Such symmetric factors can be built from smaller orthogonal matrices, which can be parameterized by standard methods. An example is included that uses the proposed parameterization for the construction of symmetric differentiable compactly supported multiwavelets. The factorization presented in this paper can be used also for finding symmetric orthogonal wavelets for an existing set of compactly supported symmetric orthogonal scaling functions.<\/jats:p>","DOI":"10.1137\/s0895479802411043","type":"journal-article","created":{"date-parts":[[2003,11,7]],"date-time":"2003-11-07T11:17:43Z","timestamp":1068203863000},"page":"532-550","source":"Crossref","is-referenced-by-count":7,"title":["An Algorithm for the Construction of Symmetric Orthogonal Multiwavelets"],"prefix":"10.1137","volume":"25","author":[{"given":"Radka","family":"Turcajov\u00e1","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,31]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"Albert Cohen, Biorthogonal wavelets, Wavelet Anal. 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