Optimal Solution of Nonlinear Equations is a text/monograph designed to provide an overview of optimal computational methods for the solution of nonlinear equations, fixed points of contractive and noncontractive mapping, and for the computation of the topological degree. It is of interest to any reader working in the area of Information-Based Complexity. The worst-case settings are analyzed here. Several classes of functions are studied with special emphasis on tight complexity bounds and methods which are close to or achieve these bounds. Each chapter ends with exercises, including companies and open-ended research based exercises.


"The volume under consideration studies the complexity of the following nonlinear problems in the worst-case setting: approximating the solution of nonlinear equations, approximating fixed points, and calculating topological degree. . . . At the end of each chapter, there are historical annotations and a bibliography. The author is a leading researcher in these areas, and well qualified to write such a monograph. The book is complete, with proofs given in full detail. . . . [T]his monograph will be a useful tool, both for those who wish to learn about complexity and optimal algorithms for nonlinear equations, as well as for those who are already working in this area." — Mathematical Reviews