A new technique in systems analysis under interval uncertainty and ambiguity.

*(English)*Zbl 1020.65029The author considers systems of equations under the aspect of interval uncertainty and/or ambiguity. His approach is crucially based on two concepts: the consequent use of logical quantifiers and a generalization of the interval arithmetic which deals also with so-called improper intervals \([a,b]\) where \(b< a\). By means of these quantities it is possible to characterize different kinds of interval uncertainties that occur in practice. Generalized intervals are used for the solution of problems which are minimax by their nature. Techniques are developed for inner and outer estimations of particular types of solution sets. Although parts of the paper are devoted to the general nonlinear case the linear systems are studied in much greater detail.

To some extent the contribution is a survey of earlier works by the author and by other researchers, but a considerable part of the results presented in 8 major chapters is new. Many smaller examples illustrate the theory which is based on a remarkable bibliography of more than 130 references.

To some extent the contribution is a survey of earlier works by the author and by other researchers, but a considerable part of the results presented in 8 major chapters is new. Many smaller examples illustrate the theory which is based on a remarkable bibliography of more than 130 references.

Reviewer: Günter Mayer (Speyer)

##### MSC:

65H10 | Numerical computation of solutions to systems of equations |

65F10 | Iterative numerical methods for linear systems |

65-00 | General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to numerical analysis |

65-02 | Research exposition (monographs, survey articles) pertaining to numerical analysis |