Journal of applied mathematics & informatics
- Volume 25 Issue 1_2
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- Pages.345-351
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- 2007
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- 2734-1194(pISSN)
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- 2234-8417(eISSN)
AN IMPROVED UNIFYING CONVERGENCE ANALYSIS OF NEWTON'S METHOD IN RIEMANNIAN MANIFOLDS
- Argyros, Ioannis K. (Department of Mathematical Sciences, Cameron University)
- Published : 2007.09.30
Abstract
Using more precise majorizing sequences we provide a finer convergence analysis than before [1], [7] of Newton's method in Riemannian manifolds with the following advantages: weaker hypotheses, finer error bounds on the distances involved and a more precise information on the location of the singularity of the vector field.
Keywords
- Newton's method;
- Riemannian manifold;
- local/semilocal convergence;
- singularity of a vector field;
- Newton-Kantorovich method