In the nearly seven years since I finished writing the first edition of this book research on the
accuracy and stability of numerical algorithms has continued to flourish and mature. Our …

Before using interval analysis as a basic tool in the following chapters, we shall now
introduce its main concepts. Section 2.2 recalls fundamental notions on set operators, set …

We give an overview on applications of interval arithmetic. Among others we discuss
verification methods for linear systems of equations, nonlinear systems, the algebraic …

Numerical analysis is an increasingly important link between pure mathematics and its
application in science and technology. This textbook provides an introduction to the …

Our aim in writing this book was to provide an extensive set of C++ programs for solving
basic numerical problems with verification of the results. This C++ Toolbox for Verified …

As suggested by the title of this book Numerical Toolbox for Verified Computing, we present
an extensive set of sophisticated tools to solve basic numerical problems with a verification …

Infimum-supremum interval arithmetic is widely used because of ease of implementation
and narrow results. In this note we show that the overestimation of midpoint-radius interval …

Since hybrid embedded systems are pervasive and often safety-critical, guarantees about
their correct performance are desirable. The hybrid systems model checker HyTech provides …

A logical statement has a value that is either true or false, t or f for short. Such statements can
be combined in logical expressions by logical operators. In this treatise the logical operators …

Interval methods for verified integration of initial value problems (IVPs) for ODEs have been
used for more than 40 years. For many classes of IVPs, these methods are able to compute …