Quasi-analytical root-finding for non-polynomial functions - Bracciali, Cleonice F. [UNESP]; Carley, Michael (Springer Nature, 2017)
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.
Keywords: Orthogonal functions; Quadrature rules; Root-finding