{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:20:05Z","timestamp":1760242805701,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2016,7,9]],"date-time":"2016-07-09T00:00:00Z","timestamp":1468022400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematics"],"abstract":"<jats:p>We focus on inverse preconditioners based on minimizing     F ( X ) = 1 \u2212 cos ( X A , I )    , where     X A     is the preconditioned matrix and A is symmetric and positive definite. We present and analyze gradient-type methods to minimize     F ( X )     on a suitable compact set. For this, we use the geometrical properties of the non-polyhedral cone of symmetric and positive definite matrices, and also the special properties of     F ( X )     on the feasible set. Preliminary and encouraging numerical results are also presented in which dense and sparse approximations are included.<\/jats:p>","DOI":"10.3390\/math4030046","type":"journal-article","created":{"date-parts":[[2016,7,11]],"date-time":"2016-07-11T09:47:19Z","timestamp":1468230439000},"page":"46","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Geometrical Inverse Preconditioning for Symmetric Positive Definite Matrices"],"prefix":"10.3390","volume":"4","author":[{"given":"Jean-Paul","family":"Chehab","sequence":"first","affiliation":[{"name":"LAMFA, UMR CNRS 7352, Universit\u00e9 de Picardie Jules Verne, 33 rue Saint Leu, 80039 Amiens, France"}]},{"given":"Marcos","family":"Raydan","sequence":"additional","affiliation":[{"name":"Departamento de C\u00f3mputo Cient\u00edfico y Estad\u00edstica, Universidad Sim\u00f3n Bol\u00edvar, Ap. 89000, Caracas 1080-A, Venezuela"}]}],"member":"1968","published-online":{"date-parts":[[2016,7,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"693","DOI":"10.1016\/j.camwa.2015.12.008","article-title":"Sparse approximate inverse preconditioners on high performance GPU platforms","volume":"71","author":"Bertaccini","year":"2016","journal-title":"Comput. 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