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Maximal Stationary Iterative Methods for the Solution of Operator Equations,
CARNEGIE-MELLON UNIV PITTSBURGH PA DEPT OF COMPUTER SCIENCE
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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 or m or infinity, the author proves that interpolatory iteration is maximal for n 0 in the class of iterations using values of the first s derivatives at n previous points. Author
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