6 citations · 11 across the 8 of their papers we have counts for
9 papers
Spiral Endgames for Computing Singular Endpoints of Homotopy Paths
Emma R. Cobian, Jonathan D. Hauenstein, Charles W. Wampler
We develop a new endgame for numerically computing singular solutions to complex analytic systems by means of a homotopy path whose endpoint is the solution to be computed. When th…
Common Real Secants to Pairs of Real Twisted Cubic Curves
Saima Aslam, Matthew Faust, Jonathan D. Hauenstein +5
It is well established that a general pair of twisted cubic curves in complex projective space has ten common secant lines. As an initial investigation, we show that the monodromy…
Robust Numerical Algebraic Geometry
Emma R. Cobian, Jonathan D. Hauenstein, Charles W. Wampler
The field of numerical algebraic geometry consists of algorithms for numerically solving systems of polynomial equations. When the system is exact, such as having rational coeffici…
Trifocal Relative Pose from Lines at Points and its Efficient Solution
Ricardo Fabbri, Timothy Duff, Hongyi Fan +8
We present a method for solving two minimal problems for relative camera pose estimation from three views, which are based on three view correspondences of i) three points and one…
On Searching for Small Kochen-Specker Vector Systems (extended version)
Felix Arends, Joel Ouaknine, Charles W. Wampler
Kochen-Specker (KS) vector systems are sets of vectors in R^3 with the property that it is impossible to assign 0s and 1s to the vectors in such a way that no two orthogonal vector…
Multiprecision path tracking
Daniel J. Bates, Andrew J. Sommese, Charles W. Wampler
A path tracking algorithm that adaptively adjusts precision is presented. By adjusting the level of precision in accordance with the numerical conditioning of the path, the algorit…
Solution of polynomial systems derived from differential equations
E. L. Allgower, D. J. Bates, A. J. Sommese +1
Nonlinear two-point boundary value problems arise in numerous areas of application. The existence and number of solutions for various cases has been studied from a theoretical stan…
Solving Polynomial Systems Equation by Equation
Andrew J. Sommese, Jan Verschelde, Charles W. Wampler
By a numerical continuation method called a diagonal homotopy we can compute the intersection of two positive dimensional solution sets of polynomial systems. This paper proposes t…
An intrinsic homotopy for intersecting algebraic varieties
Andrew J. Sommese, Jan Verschelde, Charles W. Wampler
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.…