Accession Number : AD0737327

Title :   Investigations on the Numerical Solution of Polynomial Equations.

Descriptive Note : Final technical rept. 1 Jan 71-31 Jan 72,

Corporate Author : BASEL UNIV (SWITZERLAND) MATHEMATICS INST

Personal Author(s) : Ostrowski,Alexander M.

Report Date : FEB 1972

Pagination or Media Count : 9

Abstract : An inequality for the lower Euclidean bound of a matrix, which is best in a certain sense, is derived. The monotonic property of Minkowski means is sharpened by accounting for the equality sign in the corresponding inequalities. A new characterization of Schur's complement is derived and applied to a simplified proof of Haynsworth's quotient formula. For Lipschiz mappings in Banach spaces some inequalities in the large are deduced. In an investigation of Newton's method for operator equations in Banach spaces, precise error estimates can be obtained. A new notation in the theory of divided differences allows an easier treatment of the confluent case. (Author)

Descriptors :   (*FUNCTIONAL ANALYSIS, POLYNOMIALS), INEQUALITIES, BANACH SPACE, MAPPING(TRANSFORMATIONS), MATRICES(MATHEMATICS), SWITZERLAND

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE