An intrinsic homotopy for intersecting algebraic varieties

Authors:
Andrew J. Sommese;Jan Verschelde;Charles W. Wampler
Affiliations:
Department of Mathematics, University of Notre Dame, Notre Dame, IN;Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Chicago, IL;General Motors Research and Development, Warren, MI
Venue:
Journal of Complexity - Festschrift for the 70th birthday of Arnold Schönhage
Year:
2005

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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. Three numerical experiments all show a speedup of about a factor two.