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Sweeping algebraic curves for singular solutions

✍ Scribed by Kathy Piret; Jan Verschelde

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
375 KB
Volume
234
Category
Article
ISSN
0377-0427

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✦ Synopsis

a b s t r a c t Many problems give rise to polynomial systems. These systems often have several parameters and we are interested to study how the solutions vary when we change the values for the parameters. Using predictor-corrector methods we track the solution paths. A point along a solution path is critical when the Jacobian matrix is rank deficient. The simplest case of quadratic turning points is well understood, but these methods no longer work for general types of singularities. In order not to miss any singular solutions along a path we propose to monitor the determinant of the Jacobian matrix. We examine the operation range of deflation and relate the effectiveness of deflation to the winding number. Computational experiments on systems coming from different application fields are presented.

πŸ“œ SIMILAR VOLUMES

Local and Global Zeta-Functions of Singu
Local and Global Zeta-Functions of Singular Algebraic Curves
✍ Karl-Otto StΓΆhr πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 420 KB

Let X be a complete singular algebraic curve defined over a finite field of q elements. To each local ring O of X there is associated a zeta-function `O(s) that encodes the numbers of ideals of given norms. It splits into a finite sum of partial zeta-functions, which are rational functions in q &s .