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Barycentre method for solving distance equations / X. Shuqiang in Survey review, vol 48 n° 348 (May 2016)  

Public [article]  inSurvey review > vol 48 n° 348 (May 2016) . - pp 188 - 194 Titre : Barycentre method for solving distance equations Type de document : Article/Communication Auteurs : X. Shuqiang, Auteur ; Y. Yuanxi, Auteur ; D. Yamin, Auteur Année de publication : 2016 Article en page(s) : pp 188 - 194 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Mathématique [Termes IGN] algorithme de Gauss-Newton [Termes IGN] barycentre [Termes IGN] distance [Termes IGN] équation [Termes IGN] itération [Termes IGN] méthode des moindres carrés Résumé : (auteur) When iteratively solving the distance equations, the Newton’s method has quadratic convergence but it requires the second-order derivatives. The Gauss–Newton’s method needs no information about the second-order derivatives but it may fail without the line search strategy. A simple method called barycentre method is proposed to locally solving the distance equations without the Hessian matrix, the matrix inversion and the line search strategy. The geometrical meaning of the non-linear least-squares solution of the distance equations is revealed that it is the barycentre of a particle system composed of the observational weights at the endpoints of observed distance vectors. By the geometrical meaning of the non-linear least squares, the authors structure an iterative equation to solve the distance equation, and then the convergence and the computational complexity of the method proposed is discussed. It shows that the barycentre method is a conservatively steepest decent method to guarantee the convergence and this method has good performances for solving well-conditioned problems. Ultimately, the method proposed is applied to well-condition and ill-posed positioning equations and the main results are verified. Numéro de notice : A2016-275 Affiliation des auteurs : non IGN Thématique : MATHEMATIQUE/POSITIONNEMENT Nature : Article DOI : 10.1179/1752270615Y.0000000020 En ligne : http://doi.org/10.1179/1752270615Y.0000000020 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=80824 [article]