Dynamics of Newton-like root finding methods
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Title
Dynamics of Newton-like root finding methodsDate
2022Publisher
SpringerBibliographic citation
Campos, B., Canela, J. & Vindel, P. Dynamics of Newton-like root finding methods. Numer Algor (2022). https://doi.org/10.1007/s11075-022-01474-wType
info:eu-repo/semantics/articleVersion
info:eu-repo/semantics/publishedVersionAbstract
When exploring the literature, it can be observed that the operator obtained when
applying Newton-like root finding algorithms to the quadratic polynomials z2 − c
has the same form regardless of which algorithm has ... [+]
When exploring the literature, it can be observed that the operator obtained when
applying Newton-like root finding algorithms to the quadratic polynomials z2 − c
has the same form regardless of which algorithm has been used. In this paper, we
justify why this expression is obtained. This is done by studying the symmetries of
the operators obtained after applying Newton-like algorithms to a family of degree d
polynomials p(z) = zd −c. Moreover, we provide an iterative procedure to obtain the
expression of new Newton-like algorithms. We also carry out a dynamical study of
the given generic operator and provide general conclusions of this type of methods. [-]
Is part of
Numerical Algorithms (2022)Funder Name
Universitat Jaume I | Agencia Estatal de Investigación
Project code
UJI-B2019-18 | PGC2018-095896-B-C22 | PID2020-118281GB-C32
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info:eu-repo/semantics/openAccess
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- IMAC_Articles [122]