An interval is a natural way of specifying a number that is specified only within certain tolerances. Interval analysis consists of the tools and methods needed to solve linear and nonlinear systems of equations in the presence of data uncertainties. Applications include the sensitivity analysis of solutions of equations depending on parameters, the solution of global nonlinear problems, and the verification of results obtained by finite-precision arithmetic. In this book emphasis is laid on those aspects of the theory which are useful in actual computations. On the other hand, the theory is developed with full mathematical rigor. For reader convenience, the book contains various proofs from linear algebra (Perron-Frobenius theory, M- and H-matrices) and analysis (existence of solutions to nonlinear systems).
Preface; Symbol index; 1. Basic properties of interval arithmetic; 2. Enclosures for the range of a function; 3. Matrices and sublinear mappings; 4. The solution of square linear systems of equations; 5. Nonlinear systems of equations; 6. Hull computation; References; Author index; Subject index.