Interval Analysis: and Automatic Result Verification

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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, -inflation

Linear systems of equations

Nonlinear systems of equations

Eigenvalue problems

Automatic differentiation

Complex intervals