Geodesic
Computing quaternionic roots by Newton's method
Electronic transactions on numerical analysis, Tome 26 (2007), pp. 82-102
Newton's method for finding zeros is formally adapted to finding roots of Hamilton's quaternions.
Classification : 11R52, 12E15, 30G35, 65D15
Keywords: roots of quaternions, Newton's method applied to finding roots of quaternions 
@article{ETNA_2007__26__a21,
     author = {Janovsk\'a,  Drahoslava and Opfer,  Gerhard},
     title = {Computing quaternionic roots by {Newton's} method},
     journal = {Electronic transactions on numerical analysis},
     pages = {82--102},
     year = {2007},
     volume = {26},
     zbl = {1160.65016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2007__26__a21/}
}
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%A Opfer,  Gerhard
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%J Electronic transactions on numerical analysis
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Janovská,  Drahoslava; Opfer,  Gerhard. Computing quaternionic roots by Newton's method. Electronic transactions on numerical analysis, Tome 26 (2007), pp. 82-102. http://geodesic.mathdoc.fr/item/ETNA_2007__26__a21/