An intrinsic homotopy for intersecting algebraic varieties

Details An intrinsic homotopy for intersecting algebraic varieties An intrinsic homotopy for intersecting algebraic varieties

2004-04-05

arxiv.org/abs/math/0404108v1

Mathematics

Numerical Analysis

Scientific paper

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.

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