Determination of minimum sets of the set of zeros of a function
| Autor: | J. Wolff von Gudenberg |
|---|---|
| Rok vydání: | 1980 |
| Předmět: |
Discrete mathematics
Numerical Analysis Rounding Image (category theory) Function (mathematics) Interval (mathematics) Space (mathematics) Computer Science Applications Theoretical Computer Science Interval arithmetic Combinatorics Computational Mathematics Range (mathematics) Computational Theory and Mathematics Real-valued function Software Mathematics |
| Zdroj: | Computing. 24:203-212 |
| ISSN: | 1436-5057 0010-485X |
| DOI: | 10.1007/bf02281725 |
| Popis: | Given a real function\(f:\mathbb{R} \supseteq X \to \mathbb{R}\) depending on several parametersa1, ...,an contained in elementsA1, ...,An of the extended interval-spaceℍ, see [5], [6]. One is interested in the set of zeros Open image in new window of the range Open image in new window off. According to the special problem it may be reasonable to determine inclusions or minimum sets ofNf. In the usual interval analysis mainly inclusions are determined e. g. [1], [3], [8], [9], whereas minimum sets of solutions of linear systems are treated in e. g. [2], [4]. The extension of the interval space allows to treat this problem in an algebraic straight forward way. After a short description of the extended interval spaceℍ, the definition and description of the range operator Open image in new window , in the last chapter a Newton-like algorithm, determining minimum sets is introduced, which also allows the automatic treatment of rounding errors. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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