## Novel Approaches to Numerical Software with Result Verification (2003)

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Venue: | NUMERICAL SOFTWARE WITH RESULT VERIFICATION, INTERNATIONAL DAGSTUHL SEMINAR, DAGSTUHL |

Citations: | 26 - 18 self |

### BibTeX

@INPROCEEDINGS{Granvilliers03novelapproaches,

author = {Laurent Granvilliers and Vladik Kreinovich and Norbert Müller},

title = {Novel Approaches to Numerical Software with Result Verification},

booktitle = {NUMERICAL SOFTWARE WITH RESULT VERIFICATION, INTERNATIONAL DAGSTUHL SEMINAR, DAGSTUHL},

year = {2003},

pages = {274--305},

publisher = {Springer}

}

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### Abstract

Traditional design of numerical software with result verification is based on the assumption that we know the algorithm ¦¨§� © ©���� £��������� � that transforms input © ©�� into �� � £��������� � ©���� the output, and we £��������� � know the intervals of possible values of the inputs. Many real-life problems go beyond this paradigm. In some cases, we do not have an algorithm ¦, we only know some relation (constraints) between ©� � and. In other cases, in addition to knowing the intervals, we may know some relations between; we may have some information about the probabilities of different values of © � , and we may know the exact values of some of the inputs (e.g., we may know that © £ ���¨�� �). In this paper, we describe the approaches for solving these real-life problems. In Section 2, we describe interval consistency techniques related to handling constraints; in Section 3, we describe techniques that take probabilistic information into consideration, and in Section 4, we overview techniques for processing exact real numbers.