Quasi-analytical root-finding for non-polynomial functions
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Springer Nature
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Article
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Acesso aberto
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Abstract
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.
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English
Citation
Numerical Algorithms, v. 76, n. 3, p. 639-653, 2017.
