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 Daniel Abram Brake

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Average citations per article0.40
Citation Count2
Publication count5
Publication years2012-2017
Available for download2
Average downloads per article49.50
Downloads (cumulative)99
Downloads (12 Months)77
Downloads (6 Weeks)12
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1 published by ACM
July 2017 ACM Transactions on Mathematical Software (TOMS): Volume 44 Issue 1, July 2017
Publisher: ACM
Bibliometrics:
Citation Count: 0
Downloads (6 Weeks): 10,   Downloads (12 Months): 52,   Downloads (Overall): 52

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Bertini_real is a compiled command line program for numerically decomposing the real portion of a positive-dimensional complex component of an algebraic set. The software uses homotopy continuation to solve a series of systems via regeneration from a witness set to compute a cell decomposition. The implemented decomposition algorithms are similar ...
Keywords: cell decompositions, homotopy continuation, polynomial system, real solutions, Numerical algebraic geometry

2 published by ACM
July 2016 ISSAC '16: Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation
Publisher: ACM
Bibliometrics:
Citation Count: 0
Downloads (6 Weeks): 2,   Downloads (12 Months): 25,   Downloads (Overall): 47

Full text available: PDFPDF
Computing the real solutions to a system of polynomial equations is a challenging problem, particularly verifying that all solutions have been computed. We describe an approach that combines numerical algebraic geometry and sums of squares programming to test whether a given set is "complete" with respect to the real solution ...
Keywords: polynomial solving, numerical algebraic geometry, numerical analysis, polynomials, real solutions, validation

3
November 2015 MACIS 2015: Revised Selected Papers of the 6th International Conference on Mathematical Aspects of Computer and Information Sciences - Volume 9582
Publisher: Springer-Verlag New York, Inc.
Bibliometrics:
Citation Count: 1

Globally, the solution set of a system of polynomial equations with complex coefficients can be decomposed into irreducible components. Using numerical algebraic geometry, each irreducible component is represented using a witness set thereby yielding a numerical irreducible decomposition of the solution set. Locally, the irreducible decomposition can be refined to ...
Keywords: Numerical algebraic geometry, Numerical irreducible decomposition, Numerical local irreducible decomposition, Local irreducible decomposition

4
November 2015 MACIS 2015: Revised Selected Papers of the 6th International Conference on Mathematical Aspects of Computer and Information Sciences - Volume 9582
Publisher: Springer-Verlag New York, Inc.
Bibliometrics:
Citation Count: 0

Cooperating robotic systems, especially in the context of fault-tolerance of complex robotic mechanisms, is an important question for theoretical and applied studies. In this paper, we focus on one measure of fault tolerance in robots, namely, the multiplicity of the configurations for reaching a particular point in the workspace, which ...
Keywords: Homotopy continuation, Workspace mapping, Joint failure, Monte Carlo methods

5
January 2012
Bibliometrics:
Citation Count: 0

This dissertation considers three topics that are united by the theme of application of geometric and nonlinear mechanics to practical problems. Firstly we consider the parallel implementation of numerical solution of nonlinear polynomial systems depending on parameters. The program written to do this is called Paramotopy , and uses the ...



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