6 citations · 11 across the 8 of their papers we have counts for
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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…
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…
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.…