Open AccessA note on machine method for root extraction
Author(s) -
Saroj Kumar Padhan,
Subigyan Gadtia
Publication year - 2022
Publication title -
boletim da sociedade paranaense de matemática
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.347
H-Index - 15
eISSN - 2175-1188
pISSN - 0037-8712
DOI - 10.5269/bspm.42530
Subject(s) - square root , root (linguistics) , extraction (chemistry) , extension (predicate logic) , mathematics , newton's method , simple (philosophy) , algorithm , computer science , calculus (dental) , chromatography , geometry , physics , nonlinear system , chemistry , philosophy , medicine , linguistics , dentistry , epistemology , quantum mechanics , programming language
The present investigation deals with the critical study of the works of Lancaster and Traub, who have developed $n$th root extraction methods of a real number. It is found that their developed methods are equivalent and the particular cases of Halley's and Householder's methods. Again the methods presented by them are easily obtained from simple modifications of Newton's method, which is the extension of Heron's square root iteration formula. Further, the rate of convergency of their reported methods are studied.