On the probability distribution of data at points in real complete intersection varieties
The authors are interested in the design and analysis of efficient algorithms for real solving of multi-variate real polynomial equations using probability algorithms. Basic approach stems from the ideas of a series of seminal papers by \textit{M. Shub} and \textit{S. Smale} [J. Am. Math. Soc. 6, No. 2, 459-501 (1993; Zbl 0821.65035); in: Computational algebraic geometry. Prog. Math. 109, 267--285 (1993; Zbl 0851.65031); J. Complexity 9, No. 1, 4--14 (1993; Zbl 0846.65018); SIAM J. Numer. Anal. 33, No. 1, 128--148 (1996; Zbl 0843.65035); Theor. Comput. Sci. 133, No.1, 141-164 (1994; Zbl 0846.65022)]. Thus, this paper is (using the words of the authors) a modest attempt to re-initialize this study from the most elementary aspects, i.e. study of the probability distribution of three data at points in real complete intersection varieties. (1) Norms of real affine zeros of real complete intersections. (2) Condition number at real zeros of real system of multivariate polynomial equations. (3) Convergence radius of Newton's operator at zeros of complete intersection real algebraic varieties.
scientific article; zbMATH DE number 5345369
scientific article