An intrinsic homotopy for intersecting algebraic varieties

被引：10

作者：

Sommese, AJ

Verschelde, J

Wampler, CW

机构：

[1] Univ Illinois, Dept Math Stat & Comp Sci, Chicago, IL 60607 USA

[2] Univ Notre Dame, Dept Math, Notre Dame, IN 46556 USA

[3] GM Corp, Res & Dev, Warren, MI 48090 USA

来源：

JOURNAL OF COMPLEXITY | 2005年 / 21卷 / 04期

基金：

美国国家科学基金会;

关键词：

components of solutions; embedding; generic points; homotopy continuation; irreducible components; numerical algebraic geometry; polynomial system;

D O I：

10.1016/j.jco.2004.09.007

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

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. (c) 2005 Elsevier Inc. All rights reserved.

引用

页码：593 / 608

页数：16

共 16 条

[1] ALLGOWER EL, 2003, SPRINGER SERIES COMP, V13
[2] [Anonymous], [No title captured]
[3] [Anonymous], P 2000 IEEE INT C RO
[4] Eisenbud D., 1995, Commutative Algebra with a View Toward Algebraic Geometry, V150
[5] Numerical Schubert calculus
Huber, B
Sottile, F
Sturmfels, B
[J]. JOURNAL OF SYMBOLIC COMPUTATION, 1998, 26 (06) : 767 - 788
[6] Li T. Y., 1997, Acta Numerica, V6, P399, DOI 10.1017/S0962492900002749
[7] Li T.Y., 2003, HDB NUMERICAL ANAL, VXI, P209
[8] LI TY, IN PRESS SIAM J MATR
[9] Morgan A. P., 1987, SOLVING POLYNOMIAL S
[10] MUMFORD D, 1976, GRUNDHLEHREN MATH WI, V221

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