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Some Remarks on Proof Techniques in Analytic Complexity
Strict Lower and Upper Bounds on Iterative Computational
Operator Equations by Newtons Method
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algebraic Algorithm 4.2 analytic computational complexity arithmetic assume Banach spaces Birkhoff interpolation Carnegie-Mellon University comp complexity index Computer Science Computer Science Department consider defined denote Department of Computer derivatives efficient error coefficient evaluations of f example f satisfying finite formal power series function evaluations function f given Hence Hensel incidence matrix interpolation inverse inverse quadratic interpolation itera iteration cp iteration phase Iterative Methods J. F. Traub Kung and Traub Lemma lower bounds maximal order multiple-precision multiplication multipoint iterations Newton steps Newton's method nonlinear equations Note numerical stability obtain one-point operations optimal order order of information order of iteration p-adic paper pol(n power series precision problem prove root Runge-Kutta methods Schultz search phase secant method Section Sharma 72 simple zero solve starting point technique Theorem 4.1 tion Traub 64 upper bound Winograd Wozniakowski 75b Zassenhaus zero-finding methods