Quasi-analytical root-finding for non-polynomial functions

Autor(es)

Bracciali, Cleonice F. ^[1] ; Carley, Michael ^[2]

Afiliação do(s) autor(es)

^[1] Univ Estadual Paulista, UNESP, Dept Matemat Aplicada, BR-15054000 Sao Jose Do Rio Preto, SP - Brazil

^[2] Univ Bath, Dept Mech Engn, Bath BA2 7AY, Avon - England

• Tipo de documento: Artigo Científico
• Fonte: NUMERICAL ALGORITHMS; v. 76, n. 3, p. 639-653, NOV 2017.
• Citações Web of Science: 0

Resumo

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. (AU)

• Processo FAPESP: 14/22571-2 - Polinômios ortogonais e seus similares com aplicações analíticas e numéricas
• Beneficiário: Cleonice Fátima Bracciali
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 14/17357-1 - Polinômios ortogonais e o método multipolar rápido
• Beneficiário: Cleonice Fátima Bracciali
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional