First presenter			Co-presenter(s)
Name :	Yun Guan *		Name:
E-mail:			E-mail:
Affiliation:	University of Illinois Chicago		Name:
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City:			Name:
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Country:	USA		Name:
Talk Number:	09-08		E-mail:
Session:	9- Symbolic and Numeric Computation		Schedule:   Room:	Saturday, 14:00   B-3432
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Title of presentation:	Conditioning numerical representations of algebraic sets
Abstract:
Numerical data structures for positive dimensional solution sets of polynomial system are sets of generic points cut out by random planes. We may represent the linear spaces defined by those planes either by explicit linear equations or in parametric form. These descriptions are respectively called extrinsic and intrinsic representations. Previous work by Andrew Sommese, Jan Verschelde, and Charles Wampler showed how the intrinsic formulation of diagonal homotopies reduced the cost of the linear algebra operations during path following. Via coordinate transformations we observed improved conditioning and an increased radius of convergence of Newton's method. This is work in progress joint with Jan Verschelde.