Since the introduction of the computer, numerical analysis has developed into an increasingly important connecting link between pure mathematics and its application in science and technology. Its independence as a mathematical discipline depends, above all, on two things: the justification and development of constructive methods that provide sufficiently accurate approximations to the solution of problems, and the analysis of the influence that errors in data, finite-precision calculations, and approximation formulas have on results, problem formulation, and the choice of method. This book provides an introduction to these themes.

A novel feature of this book is the consequent development of interval analysis as a tool for rigorous computation and computer-assisted proofs. Apart from this, most of the material treated can be found in typical textbooks on numerical analysis; but even then, proofs may be shorter than and the perspective may be different from those elsewhere. Some of the material on nonlinear equations presented here previously appeared only in specialized books or in journal articles.

Readers are expected to have a background knowledge of matrix algebra and calculus of several real variables, and to know just enough about topological concepts to understand that sequences in a compact subset in ℝn have a convergent subsequence. In a few places, elements of complex analysis are used.

The book is based on course lectures in numerical analysis that the author gave repeatedly at the University of Freiburg (Germany) and the University of Vienna (Austria).