Abstract
It is known that Gröbner bases approach can be useful to solve systems of algebraic equations with a finite number of solutions. Nevertheless, as stated in [Bu], numerical accuracy attainable when using floating point arithmetic is not yet studied. In this paper we discuss numerical approach, defining conveniently the condition number of every root, and the numerical g.c.d.'s of Buchberger's algorithm. With these instruments we are able to compute confidence-intervals for the roots. We complete the study with two illustrative examples. We also give some insight about the best order of the variables when pure lexicographical order is concerned.
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