Bibliographic Details
| Title: |
Simple varieties for limited precision points. |
| Authors: |
Fassino, Claudia1 fassino@dima.unige.it, Torrente, Maria-Laura1 torrente@dima.unige.it |
| Source: |
Theoretical Computer Science. Apr2013, Vol. 479, p174-186. 13p. |
| Subjects: |
Precision (Information retrieval), Set theory, Finite element method, Numerical analysis, Combinatorics, Algebra software |
| Abstract: |
Abstract: Given a finite set of points and a tolerance representing the maximum error on the coordinates of each point, we address the problem of computing a simple polynomial whose zero-locus “almost” contains the points of . We propose a symbolic–numerical method that, starting from the knowledge of and , determines a polynomial whose degree is strictly bounded by the minimal degree of the elements of the vanishing ideal of . Then, in Theorem 4.3, we state the sufficient conditions for proving that lies close to each point of by less than . The validity of the proposed method relies on a combination of classical results of Computer Algebra and Numerical Analysis; its effectiveness is illustrated with a number of examples. [Copyright &y& Elsevier] |
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| Database: |
Engineering Source |
