Investigations on the Numerical Solution of Polynomial Equations.
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1972
- Accession Number
- AD0737327
Entities
People
- Alexander M. Ostrowski
Organizations
- University of Basel