Investigations on the Numerical Solution of Polynomial Equations.
Final technical rept. 1 Jan 71-31 Jan 72,
BASEL UNIV (SWITZERLAND) MATHEMATICS INST
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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 Schurs complement is derived and applied to a simplified proof of Haynsworths quotient formula. For Lipschiz mappings in Banach spaces some inequalities in the large are deduced. In an investigation of Newtons 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
- Theoretical Mathematics