Interval Analysis: and Automatic Result Verification

This self-contained text is a step-by-step introduction and a complete overview of interval computation and result verification, a subject whose importance has steadily increased over the past many years. The author, an expert in the field, gently presents the theory of interval analysis through many examples and exercises, and guides the reader from the basics of the theory to current research topics in the mathematics of computation.

Contents

• Preliminaries
• Real intervals
• Interval vectors, interval matrices
• Expressions, P-contraction, ε-inflation
• Linear systems of equations
• Nonlinear systems of equations
• Eigenvalue problems
• Automatic differentiation
• Complex intervals

• A self-contained introduction to the field of interval computation
• Covers automatic result verification and relevant algorithms
• An up-to-date and didactic overview of a subject underlying computer mathematics and scientific computing