caa a22 4500 44533164X CHVBK 20180317142739.0 cr unu---uuuuu 170323e20111001xx s 000 0 eng 10.1007/s10208-011-9097-1 doi (NATIONALLICENCE)springer-10.1007/s10208-011-9097-1 Khovanskii-Rolle Continuation for Real Solutions [Elektronische Daten] [Daniel Bates, Frank Sottile] We present a new continuation algorithm to find all real solutions to a nondegenerate system of polynomial equations. Unlike homotopy methods, the algorithm is not based on a deformation of the system; instead, it traces real curves connecting the solutions to 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 to the original equations. The number of curves traced is essentially bounded above by the fewnomial bound for real solutions, and the method takes advantage of any slack in that bound. SFoCM, 2011 Fewnomial nationallicence Khovanskii-Rolle nationallicence Gale dual nationallicence Homotopy nationallicence Continuation nationallicence Polynomial system nationallicence Numerical algebraic geometry nationallicence Real algebraic geometry nationallicence Bates Daniel Department of Mathematics, Colorado State University, 101 Weber Building, 80523-1874, Fort Collins, CO, USA aut Sottile Frank Department of Mathematics, Texas A&M University, 77843, College Station, TX, USA aut Foundations of Computational Mathematics Springer-Verlag 11/5(2011-10-01), 563-587 1615-3375 11:5<563 2011 11 10208 https://doi.org/10.1007/s10208-011-9097-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10208-011-9097-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bates Daniel Department of Mathematics, Colorado State University, 101 Weber Building, 80523-1874, Fort Collins, CO, USA aut NATIONALLICENCE 700 1- Sottile Frank Department of Mathematics, Texas A&M University, 77843, College Station, TX, USA aut NATIONALLICENCE 773 0- Foundations of Computational Mathematics Springer-Verlag 11/5(2011-10-01), 563-587 1615-3375 11:5<563 2011 11 10208 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer