On approximate methods of tangent hyperbolas

For solving a nonlinear operator equation in Banach space setting approximate variants of the method of tangent hyperbolas are considered. This family of approximate methods includes as special cases methods based on the use of iterative methods to obtain a cheap solution of limited accuracy for associated linear equations at each iteration step as well. A local convergence theorem and rate of convergence for the methods under discussion are given. Computational aspects and possibilities of organizing parallel computation are discussed. Computational experience with various multiprocessors indicates that performance of parallel methods depends critically on efficient load balancing. Problems of allocating subproblems to the processors are also briefly discussed.

Abstract licence: CC BY

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