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"This volume reviews, in the context of partial differential equations, algorithm development that has been specifically aimed at computers that exhibit some form of parallelism. Emphasis is on the solution of PDEs because these are typically the problems that generate high computational demands. The authors discuss architectural features of these computers insomuch as they influence algorithm performance, and provide insight into algorithm characteristics that allow effective use of hardware."

""This is a concise account of certain topics in numerical analysis which a student is expected to know when he reaches an advanced course yet may not have been introduced to in his first course on the subject...This book is organized around the notion of error. After the concepts of stability and ill-conditioning (important in gauging the effects of all kinds of error) are elucidated in a first part of the book, discretization error, convergence error, and rounding error are each studied separately in a few important situations in the last three parts of the book. A review chapter on the Jordan canonical form and on norms for vectors and matrices precedes all." -- Mathematics of Computation, July 1973, page 669. "An excellent textbook at the advanced undergraduate or beginning graduate level dealing mainly with questions of stability and growth of error. . . . . . . There are a number of books available whose content intersects significantly with Ortega's material. . . . . However, Ortega's approach is somewhat different, utilizing the concepts of stability and error growth as they arise in various computational areas to unify the treatment, rather than separately dealing with the solution of linear systems, the eigenproblem, or differential equations." -- Choice, January 1973, page 331. "The selection of the material, its presentation with many examples, and, in particular, counterexamples, make this book extremely valuable--not only for students." -- G. Mayer, Zentrablatt fur Mathematik, 1990."

"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."