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Kluwer nonconvex optimization series 
Abstract: Compiler support for interval arithmetic requires a specification of both the syntax and semantics of the implementation. The Fortran 77 specification contained herein defines a set of extended real intervals and their internal representation for IEEE 754 compliant processors. The defined set of extended real intervals is closed with respect to arithmetic operations and interval enclosures of real functions.
Abstract: Three extended real interval systems are defined and distinguished by their implementation complexity and result sharpness. The three systems are closed with respect to interval arithmetic and the enclosure of functions and relations, notwithstanding domain restrictions or the presence of singularities.
Abstract: Alternatives are considered for constructing interval enclosures of real functions with finite domains.
Abstract: Algebra of interval variables, together with composites of interval functions and relations are used to justify transformations that a compiler may automatically apply to interval expressions. A generalization of the fundamental theorem of interval arithmetic, as well as the valueassignment and expression assignment operators are used to rationalize interval expression folding.
 Abstract: A proposal is made to provide compiler support for interval arithmetic with inline code generation and nonstop exception handling. The proposal satisfies the fundamental containment requirement of interval arithmetic and produces sharp results without sacrificing performance whenever possible.
Abstract: Returning "NotanInterval", NaI, "NotaRealInterval", NaRI, or the entire extended complex plane, C^{n}, are neither required not desirable in the implementation of an extended real interval system.
Abstract: The utility of implicitly intersecting interval enclosure augments domain of definition of the enclosed function is illustrated using the interval Newton method.
Abstract:An algorithm is developed for computing X^{Y} for negative values of X.
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Kluwer nonconvex optimization series 