论文信息 - Convergence and complexity of interpolatory—newton iteration in a Banach space☆

Convergence and complexity of interpolatory—newton iteration in a Banach space☆

Abstract The class of interpolatory—Newton iterations is defined and analyzed for the computation of a simple zero of a non-linear operator in a Banach space of finite or infinite dimension. Convergence of the class is established. The concepts of “informationally optimal class of algorithms” and “optimal algorithm” are formalized. For the multivariate case, the optimality of Newton iteration is established in the class of one-point iterations under an “equal cost assumption”.

Joseph F. Traub | Henryk Woźniakowski | H. Wozniakowski | J. Traub

[1] H. Woźniakowski,et al. Numerical stability for solving nonlinear equations , 1976 .

[2] Richard M. Karp,et al. Complexity of Computation , 1974 .

[3] Richard P. Brent,et al. A CLASS OF OPTIMAL-ORDER ZERO-FINDING METHODS USING DERIVATIVE EVALUATIONS , 1976 .

[4] H. T. Kung,et al. Fast Algorithms for Manipulating Formal Power Series , 1978, JACM.

[5] H. Wozniakowski,et al. STRICT LOWER AND UPPER BOUNDS ON ITERATIVE COMPUTATIONAL COMPLEXITY , 1976 .

[6] Henryk Wozniakowski,et al. Convergence and Complexity of Newton Iteration for Operator Equations , 1979, JACM.

[7] H. Wozniakowski,et al. Generalized Information and Maximal Order of Iteration for Operator Equations , 1975 .

[8] L. B. Rall,et al. Computational Solution of Nonlinear Operator Equations , 1969 .