Accession Number : AD0758154

Title :   On Newton's Method in Banach Spaces.

Descriptive Note : Mathematical notes,

Corporate Author : BASEL UNIV (SWITZERLAND) MATHEMATICS INST

Personal Author(s) : Ostrowski,A. M.

Report Date : FEB 1972

Pagination or Media Count : 42

Abstract : In BMN 26 the error estimates for Newton's 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 Newton's 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)

Descriptors :   (*ITERATIONS, *BANACH SPACE), (*NUMERICAL METHODS AND PROCEDURES, ERRORS), HILBERT SPACE, POLYNOMIALS, INEQUALITIES, THEOREMS, SWITZERLAND

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE