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More exactly, using sparse matrix approximations, the revision term is embedded to the model for penalizing the ill-conditioning in the computational trajectory to obtain the factorization elements. Then, as an extension of the Euclidean norm, we employ the ellipsoid norm to gain adaptive formulas for the Dai\u2013Liao parameter in a least-squares framework. In essence, the parametric choices here are obtained by pushing the Dai\u2013Liao direction to the direction of a well-functioning three-term conjugate gradient algorithm. In our scheme, the well-known BFGS and DFP quasi\u2013Newton updating formulas are used to characterize the positive definite matrix factor of the ellipsoid norm. To see at what level our model revisions as well as our algorithmic modifications are effective, we seek some numerical evidence by conducting classic computational tests and assessing the outputs as well. As reported, the results weigh enough value on our analytical efforts.<\/jats:p>","DOI":"10.1007\/s11075-024-01886-w","type":"journal-article","created":{"date-parts":[[2024,7,24]],"date-time":"2024-07-24T11:02:18Z","timestamp":1721818938000},"page":"505-519","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["On solving a revised model of the nonnegative matrix factorization problem by the modified adaptive versions of the Dai\u2013Liao method"],"prefix":"10.1007","volume":"99","author":[{"given":"Saman","family":"Babaie-Kafaki","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fatemeh","family":"Dargahi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zohre","family":"Aminifard","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,7,24]]},"reference":[{"issue":"3","key":"1886_CR1","doi-asserted-by":"publisher","first-page":"681","DOI":"10.1007\/s10589-021-00286-3","volume":"79","author":"M Ahookhosh","year":"2021","unstructured":"Ahookhosh, M., Hien, L.T.K., Gillis, N., Patrinos, P.: Multi-block Bregman proximal alternating linearized minimization and its application to orthogonal nonnegative matrix factorization. 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