Maximal order of multipoint iterations using n evaluations
نویسندگان
چکیده
This paper deals with multipoint iterations without memory for the solution of the nonlinear scalar equation (m) f (x) = 0, m ^ 0. Let P n( ) be the maximal order of iterations which use n evaluations of the function or its derivatives per step. We prove the Kung and Traub conjecture p (0) = 2 n ^ for Hermitian information. We show p (m+l)^p (m) and conjecture P n( ) = 2 . The problem of the maximal order is connected with Birkhoff interpolation. Under a certain assumption we prove that the Polya conditions are necessary for maximal order.
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