000097392 001__ 97392 000097392 005__ 20230622083323.0 000097392 0247_ $$2doi$$a10.3390/math8122197 000097392 0248_ $$2sideral$$a121777 000097392 037__ $$aART-2020-121777 000097392 041__ $$aeng 000097392 100__ $$aGonzalez-Diaz, R. 000097392 245__ $$aNeural-network-based curve fitting using totally positive rational bases 000097392 260__ $$c2020 000097392 5060_ $$aAccess copy available to the general public$$fUnrestricted 000097392 5203_ $$aThis paper proposes a method for learning the process of curve fitting through a general class of totally positive rational bases. The approximation is achieved by finding suitable weights and control points to fit the given set of data points using a neural network and a training algorithm, called AdaMax algorithm, which is a first-order gradient-based stochastic optimization. The neural network presented in this paper is novel and based on a recent generalization of rational curves which inherit geometric properties and algorithms of the traditional rational Bézier curves. The neural network has been applied to different kinds of datasets and it has been compared with the traditional least-squares method to test its performance. The obtained results show that our method can generate a satisfactory approximation. 000097392 536__ $$9info:eu-repo/grantAgreement/ES/MICINN-FEDER/PID2019-107339GB-I00$$9info:eu-repo/grantAgreement/ES/MCIU-AEI/PGC2018-096321-B-I00$$9info:eu-repo/grantAgreement/ES/DGA-FEDER/Construyendo Europa desde Aragón 000097392 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/ 000097392 590__ $$a2.258$$b2020 000097392 591__ $$aMATHEMATICS$$b24 / 330 = 0.073$$c2020$$dQ1$$eT1 000097392 592__ $$a0.495$$b2020 000097392 593__ $$aMathematics (miscellaneous)$$c2020$$dQ2 000097392 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000097392 700__ $$0(orcid)0000-0002-1101-6230$$aMainar, E.$$uUniversidad de Zaragoza 000097392 700__ $$aPaluzo-Hidalgo, E. 000097392 700__ $$0(orcid)0000-0001-9130-0794$$aRubio, B.$$uUniversidad de Zaragoza 000097392 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada 000097392 773__ $$g8, 12 (2020), 2197 [1-19]$$pMathematics (Basel)$$tMathematics$$x2227-7390 000097392 8564_ $$s569854$$uhttps://zaguan.unizar.es/record/97392/files/texto_completo.pdf$$yVersión publicada 000097392 8564_ $$s491725$$uhttps://zaguan.unizar.es/record/97392/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000097392 909CO $$ooai:zaguan.unizar.es:97392$$particulos$$pdriver 000097392 951__ $$a2023-06-21-15:03:27 000097392 980__ $$aARTICLE