Maximal Stationary Iterative Methods for the Solution of Operator Equations,

摘要

The author studies stationary iterative methods of maximal order for calculating zeros of operator equations. These methods use the values of the operator and its first s Frechet derivatives at n previous iteration points. A sufficient condition is introduced for an iterative method to have maximal order in a certain class of admissible methods. The maximality of the interpolatory method (I sub n,s) is proved in the scalar case. For the m dimensional case, 2