Details:
Title  Structures of precision losses in computing approximate Gröbner bases  Author(s)  Ye Liang  Type  Article in Journal  Abstract  In computing approximate Gröbner bases, it is not easy to trace precision losses of floatingpoint coefficients of intermediate approximate polynomials. The measured precision losses are usually much larger than their genuine values. One reason causing this phenomenon is that most existing methods for tracing precision losses do not consider the dependence of such precision losses in any polynomial (as an equation). In this paper, we define an algebraic structure called PLspace (precision loss space) for a polynomial (as an equation) and set up a theory for it. We prove that any PLspace has a finite weak basis and a strong basis and show how they effect on tracing precision losses by an example. Based on the study of minimal strong bases, we propose the concept of dependence number which reveals the complexity of the dependence of precision losses in a polynomial.  Keywords  Gröbner basis, Approximate, Floatingpoint, Precision loss, PLspace  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717112001915 
Language  English  Journal  Journal of Symbolic Computation  Volume  53  Number  0  Pages  81  95  Year  2013  Edition  0  Translation 
No  Refereed 
No 
