Khovanskii-Rolle continuation for real solutions Export

@article{citeulike:5695533, abstract = {We present a new continuation algorithm to find all nondegenerate real solutions to a system of polynomial equations. Unlike homotopy methods, it is not based on a deformation of the system; instead, it traces real curves connecting the solutions of one system of equations to those of another, eventually leading to the desired real solutions. It also differs from homotopy methods in that it follows only real paths and computes no complex solutions of the original equations. The number of curves traced is bounded by the fewnomial bound for real solutions, and the method takes advantage of any slack in that bound.}, archivePrefix = {arXiv}, author = {Bates, Dan and Sottile, Frank}, citeulike-article-id = {5695533}, citeulike-linkout-0 = {http://arxiv.org/abs/0908.4579}, citeulike-linkout-1 = {http://arxiv.org/pdf/0908.4579}, day = {31}, eprint = {0908.4579}, keywords = {algebraic\_geometry, fewnomials, root\_location}, month = {Aug}, posted-at = {2009-09-01 07:12:07}, priority = {3}, title = {Khovanskii-Rolle continuation for real solutions}, url = {http://arxiv.org/abs/0908.4579}, year = {2009} }

TY - JOUR ID - citeulike:5695533 L3 - citeulike-article-id:5695533 N2 - We present a new continuation algorithm to find all nondegenerate real solutions to a system of polynomial equations. Unlike homotopy methods, it is not based on a deformation of the system; instead, it traces real curves connecting the solutions of one system of equations to those of another, eventually leading to the desired real solutions. It also differs from homotopy methods in that it follows only real paths and computes no complex solutions of the original equations. The number of curves traced is bounded by the fewnomial bound for real solutions, and the method takes advantage of any slack in that bound. TI - Khovanskii-Rolle continuation for real solutions KW - algebraic_geometry KW - fewnomials KW - root_location AU - Bates, Dan AU - Sottile, Frank PY - 2009/Aug/31/ UR - http://arxiv.org/abs/0908.4579 ER -