On Newton's Method in Banach Spaces.
BASEL UNIV (SWITZERLAND) MATHEMATICS INST
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In BMN 26 the error estimates for Newtons method were obtained which were precise in the case of numerical equations. In the present article the author develops the convergence and error theorem of Newtons method in the general case of operator equations in a Banach space and obtains precise error estimates. The convergence as the unicity theorems are developed in another direction in order to make the geometric setting of the theory less rigid. Finally, the characterization of equations, for which the equality sign in the error estimates holds, could be pushed almost as far as in the numerical case using the concept of a strictly normed space. Author Modified Abstract
- Theoretical Mathematics