Applied and Computational Mathematics and Statistics
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 Creator(s):
 Jonathan Hauenstein, Samantha Sherman
 Description:
Synthesis problems for linkages in kinematics often yield large structured parameterized polynomial systems which generically have far fewer solutions than traditional upper bounds would suggest. This paper describes statistical models for estimating the generic number of solutions of such parameterized polynomial systems. The new approach extends previous work on success ratios of parameter homotopies to using monodromy loops as well as the addition of a trace test that provides a stopping…
 Date Created:
 20200421
 Record Visibility:
 Public

2
Dataset
 Creator(s):
 Samantha Sherman, Jonathan Hauenstein
 Description:
Computational tools in numerical algebraic geometry can be used to numerically approximate solutions to a system of polynomial equations. If the system is wellconstrained (i.e., square), Newton’s method is locally quadratically convergent near each nonsingular solution. In such cases, Smale’s alpha theory can be used to certify that a given point is in the quadratic convergence basin of some solution. This was extended to certifiably determine the reality of the corresponding sol…
 Date Created:
 20180308
 Record Visibility:
 Public