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Now welcome, the most inspiring book today from a very professional writer in the world, numerical solution of systems of polynomials arising in engineering and science. This is the book that manyâ€¦ (More)

- Daniel J. Bates, Andrew J. Sommese, Jonathan D. Hauenstein, Charles W. Wampler
- Software, environments, tools
- 2013

Numerically Solving Polynomial Systems with Bertini â€¢ approaches numerical algebraic geometry from a user's point of view with many worked examples, â€¢ teaches how to use Bertini and includes aâ€¦ (More)

- Steven M. Wise, Andrew J. Sommese, Layne T. Watson
- ACM Trans. Math. Softw.
- 2000

Globally convergent, probability-one homotopy methods have proven to be very effective for finding all the isolated solutions to polynomial systems of equations. After many years of development,â€¦ (More)

- Andrew J. Sommese, Jan Verschelde
- J. Complexity
- 2000

Many applications modeled by polynomial systems have positive dimensional solution components (e.g., the path synthesis problems for four-bar mechanisms) that are challenging to compute numericallyâ€¦ (More)

- Daniel J. Bates, Jonathan D. Hauenstein, Andrew J. Sommese, Charles W. Wampler
- SIAM J. Numerical Analysis
- 2008

This article treats numerical methods for tracking an implicitly defined path. The numerical precision required to successfully track such a path is difficult to predict a priori, and indeed, it mayâ€¦ (More)

- Jonathan D. Hauenstein, Andrew J. Sommese, Charles W. Wampler
- Math. Comput.
- 2011

We present a new technique, based on polynomial continuation, for solving systems of n polynomials in N complex variables. The method allows equations to be introduced one-by-one or in groups,â€¦ (More)

- Ashraf N. Al-Khateeb, Joseph M. Powers, +4 authors J. D. Mengers
- The Journal of chemical physics
- 2009

A reactive system's slow dynamic behavior is approximated well by evolution on manifolds of dimension lower than that of the full composition space. This work addresses the construction ofâ€¦ (More)

- Eugene L. Allgower, Derrick J. Bates, Andrew J. Sommese, Charles W. Wampler
- Computing
- 2005

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 standpoint. Theseâ€¦ (More)

- Andrew J. Sommese, Jan Verschelde, Charles W. Wampler
- Theor. Comput. Sci.
- 2004

One can consider the problem of factoring multivariate complex polynomials as a special case of the decomposition of a pure dimensional solution set of a polynomial system into irreducibleâ€¦ (More)

- Jonathan D. Hauenstein, Andrew J. Sommese, Charles W. Wampler
- Applied Mathematics and Computation
- 2011

A key step in the numerical computation of the irreducible decomposition of a polynomial system is the computation of a witness superset of the solution set. In many problems involving a solution setâ€¦ (More)