Quasi-analytical root-finding for non-polynomial functions

Made available in DSpace on 2018-12-11T16:46:02Z (GMT). No. of bitstreams: 0 Previous issue date: 2017-11-01Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)A method is presented for the calculation of roots of non-polynomial functions, motivated by the requirement to generate quadrature rules based on non-polynomial orthogonal functions. The approach uses a combination of local Taylor expansions and Sturm’s theorem for roots of a polynomial which together give a means of efficiently generating estimates of zeros which can be polished using Newton’s method. The technique is tested on a number of realistic problems including some chosen to be highly oscillatory and to have large variations in amplitude, both of which features pose particular challenges to root–finding methods.Departamento de Matemática Aplicada UNESP–University Estadual PaulistaDepartment of Mechanical Engineering University of BathDepartamento de Matemática Aplicada UNESP–University Estadual PaulistaFAPESP: 2014/17357-1FAPESP: 2014/22571-

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