Iterative Solution of Nonlinear Equations in Several Variables provides a survey of the theoretical results on systems of nonlinear equations in finite dimension and the major iterative methods for their computational solution. Originally published in 1970, it offers a research-level presentation of the principal results known at that time. Although the field has developed since the book originally appeared, it remains a major background reference for the literature before 1970. In particular, Part II contains the only relatively complete introduction to the existence theory for finite-dimensional nonlinear equations from the viewpoint of computational mathematics. Over the years semilocal convergence results have been obtained for various methods, especially with an emphasis on error bounds for the iterates. The results and proof techniques introduced here still represent a solid basis for this topic.

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James M. Ortega is Professor Emeritus at the University of Virginia and currently teaches in the Department of Mathematical Sciences at the Florida Institute of Technology. He is the author of nine books and more than 40 papers. Werner C. Rheinboldt is Professor Emeritus at the University of Pittsburgh. He has written five books and over 130 papers in the areas of numerical analysis, computer science, engineering applications, ordinary and partial differential equations, and differential algebraic equations.

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