An intrinsic homotopy for intersecting algebraic varieties
Abstract
Recently we developed a diagonal homotopy method to compute a numerical representation of all positive dimensional components in the intersection of two irreducible algebraic sets. In this paper, we rewrite this diagonal homotopy in intrinsic coordinates, which reduces the number of variables, typically in half. This has the potential to save a significant amount of computation, especially in the iterative solving portion of the homotopy path tracker. There numerical experiments all show a speedup of about a factor two.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 April 2004
 arXiv:
 arXiv:math/0404108
 Bibcode:
 2004math......4108S
 Keywords:

 Numerical Analysis;
 Algebraic Geometry;
 65H10;
 13P05;
 14Q99;
 68W30