C. W. Wampler
C. W. Wampler

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Average citations per article8.07
Citation Count218
Publication count27
Publication years1990-2017
Available for download2
Average downloads per article169.00
Downloads (cumulative)338
Downloads (12 Months)60
Downloads (6 Weeks)11
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27 results found Export Results: bibtexendnoteacmrefcsv

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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

Full text available: PDFPDF
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
January 2017 Applied Mathematics and Computation: Volume 293 Issue C, January 2017
Publisher: Elsevier Science Inc.
Bibliometrics:
Citation Count: 0

The solution set of a system of polynomial equations, called an algebraic set, can be decomposed into finitely many irreducible components. In numerical algebraic geometry, irreducible algebraic sets are represented by witness sets, whereas general algebraic sets allow a numerical irreducible decomposition comprising a collection of witness sets, one for ...
Keywords: 14Q99, Algebraic set, Regeneration, 65H10, 68W30, Intersection, Numerical algebraic geometry, Witness set

3
March 2014 Applied Mathematics and Computation: Volume 231 Issue C, March 2014
Publisher: Elsevier Science Inc.
Bibliometrics:
Citation Count: 0

Systems of polynomial equations arise throughout mathematics, engineering, and the sciences. It is therefore a fundamental problem both in mathematics and in application areas to find the solution sets of polynomial systems. The focus of this paper is to compare two fundamentally different approaches to computing and representing the solutions ...
Keywords: Polynomial system, Homotopy continuation, Computational algebraic geometry, Numerical computation, Primary decomposition, Symbolic computation

4
March 2014 Applied Mathematics and Computation: Volume 231, March, 2014
Publisher: Elsevier Science Inc.
Bibliometrics:
Citation Count: 1

Systems of polynomial equations arise throughout mathematics, engineering, and the sciences. It is therefore a fundamental problem both in mathematics and in application areas to find the solution sets of polynomial systems. The focus of this paper is to compare two fundamentally different approaches to computing and representing the solutions ...
Keywords: Symbolic computation, Polynomial system, Homotopy continuation, Computational algebraic geometry, Numerical computation, Primary decomposition

5
November 2013
Bibliometrics:
Citation Count: 26

This book is a guide to concepts and practice in numerical algebraic geometry - the solution of systems of polynomial equations by numerical methods. The authors show how to apply the well-received and widely used open-source Bertini software package to compute solutions, including a detailed manual on syntax and usage ...

6
August 2013 Numerical Algorithms: Volume 63 Issue 4, August 2013
Publisher: Springer-Verlag New York, Inc.
Bibliometrics:
Citation Count: 4

Let Z be a two dimensional irreducible complex component of the solution set of a system of polynomial equations with real coefficients in N complex variables. This work presents a new numerical algorithm, based on homotopy continuation methods, that begins with a numerical witness set for Z and produces a ...
Keywords: Algebraic surface, Cell decomposition, Algebraic curve, Homotopy, Numerical algebraic geometry, Polynomial system

7
June 2013 Foundations of Computational Mathematics: Volume 13 Issue 3, June 2013
Publisher: Springer-Verlag New York, Inc.
Bibliometrics:
Citation Count: 0

This article introduces the concept of isosingular sets, which are irreducible algebraic subsets of the set of solutions to a system of polynomial equations constructed by taking the closure of points with a common singularity structure. The definition of these sets depends on deflation, a procedure that uses differentiation to ...
Keywords: Deflation sequence, Irreducible algebraic set, Isosingular point, 13P05, 68W30, Local dimension, Numerical algebraic geometry, Polynomial system, Witness set, 14Q99, Isosingular local dimension, Isosingular set, Multiplicity, Witness point, 65H10, Deflation

8
February 2013 International Journal of Robotics Research: Volume 32 Issue 2, February 2013
Publisher: Sage Publications, Inc.
Bibliometrics:
Citation Count: 1

To facilitate human assembly tasks, Robonaut 2 is equipped with a dexterous, compact hand featuring fingers driven remotely by tendons. This work outlines the force-control strategy for the fingers, which are actuated by an �€œn + 1�€ tendon arrangement. Existing tendon-driven fingers have applied force control through independent tension controllers ...
Keywords: Force control, multifingered hands, tendon actuation, humanoid robots, manipulation

9
January 2013 Applied Mathematics and Computation: Volume 219 Issue 10, January, 2013
Publisher: Elsevier Science Inc.
Bibliometrics:
Citation Count: 1

The fundamental construct of numerical algebraic geometry is the representation of an irreducible algebraic set, A, by a witness set, which consists of a polynomial system, F, for which A is an irreducible component of V(F), a generic linear space L of complementary dimension to A, and a numerical approximation ...
Keywords: Isosingular set, Deflation, Diagonal homotopy, Numerical algebraic geommetry, Irreducible algebraic set, Intersection, Polynomial system, Witness set

10
June 2011 WG'11: Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
Publisher: Springer-Verlag
Bibliometrics:
Citation Count: 2

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 vectors are assigned 0 and no three mutually orthogonal vectors are assigned 1. The existence of ...
Keywords: Kochen-Specker vector systems, constraint solving, topological graph embedding problems, graph enumeration algorithms

11
May 2008 Foundations of Computational Mathematics: Volume 8 Issue 2, May 2008
Publisher: Springer-Verlag New York, Inc.
Bibliometrics:
Citation Count: 3

Exceptional sets where fibers have dimensions higher than the generic fiber dimension are of interest in mathematics and in application areas, such as the theory of overconstrained mechanisms.We show that fiber products promote such sets to become irreducible components, whereupon they can be found using techniques from numerical algebraic geometry ...

12
April 2008 Foundations of Computational Mathematics: Volume 8 Issue 2, April 2008
Publisher: Springer-Verlag New York, Inc.
Bibliometrics:
Citation Count: 0

Exceptional sets where fibers have dimensions higher than the generic fiber dimension are of interest in mathematics and in application areas, such as the theory of overconstrained mechanisms.We show that fiber products promote such sets to become irreducible components, whereupon they can be found using techniques from numerical algebraic geometry ...

13
February 2008 SIAM Journal on Numerical Analysis: Volume 46 Issue 2, March 2008
Publisher: Society for Industrial and Applied Mathematics
Bibliometrics:
Citation Count: 18

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 may change dramatically through the course of the path. In current practice, one must either choose a conservatively large numerical ...
Keywords: homotopy continuation, Bertini, numerical algebraic geometry, polynomial systems

14 published by ACM
July 2007 SNC '07: Proceedings of the 2007 international workshop on Symbolic-numeric computation
Publisher: ACM
Bibliometrics:
Citation Count: 0
Downloads (6 Weeks): 1,   Downloads (12 Months): 8,   Downloads (Overall): 286

Full text available: PDFPDF
Numerical algebraic geometry uses numerical methods, principally numerical tracking of paths defined by polynomial homotopies, to find and manipulate algebraic sets defined by systems of polynomial equations. Kinematics is the study of the geometrical aspects of mechanical motion. The kinematical problems arising in the analysis and design of most robots ...
Keywords: homotopy continuation, numerical algebraic geometry, kinematics, robotics

15
January 2006 Computing: Volume 76 Issue 1, January 2006
Publisher: Springer-Verlag New York, Inc.
Bibliometrics:
Citation Count: 6

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. These results generally rely upon growth conditions of the nonlinearity. However, in general, one cannot forecast how many solutions a boundary value problem ...
Keywords: Differential equations, homotopy continuation, numerical algebraic geometry, polynomial systems, boundary value problems

16
August 2005 Journal of Complexity - Festschrift for the 70th birthday of Arnold Schönhage: Volume 21 Issue 4, August 2005
Publisher: Academic Press, Inc.
Bibliometrics:
Citation Count: 3

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. In this paper, we rewrite this diagonal homotopy in intrinsic coordinates, which reduces the number of variables, typically in half. This has the potential to ...
Keywords: Components of solutions, Generic points, Irreducible components, 68W30, Embedding, Numerical algebraic geometry, Polynomial system, 14Q99, Homotopy continuation, primary 65H10, secondary 13P05

17
August 2005 Journal of Complexity - Festschrift for the 70th birthday of Arnold Schönhage: Volume 21 Issue 4, August 2005
Publisher: Academic Press, Inc.
Bibliometrics:
Citation Count: 0

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. In this paper, we rewrite this diagonal homotopy in intrinsic coordinates, which reduces the number of variables, typically in half. This has the potential to ...
Keywords: embedding, homotopy continuation, generic points, irreducible components, numerical algebraic geometry, components of solutions, polynomial system

18
May 2004 Theoretical Computer Science - Algebraic and numerical algorithm: Volume 315 Issue 2-3, 6 May 2004
Publisher: Elsevier Science Publishers Ltd.
Bibliometrics:
Citation Count: 16

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 irreducible components. The importance and nature of this problem however justify a special treatment. We exploit the reduction to the univariate root ...
Keywords: approximate factorization, homotopy continuation, symbolic-numeric computation, witness points, Newton interpolation, generic points, irreducible decomposition, numerical algebraic geometry, Stewart-Gough platform, divided differences, multiple roots, monodromy, polynomial, traces

19
April 2004 SIAM Journal on Numerical Analysis: Volume 42 Issue 4, 2004
Publisher: Society for Industrial and Applied Mathematics
Bibliometrics:
Citation Count: 11

We show how to use numerical continuation to compute the intersection $C=A\cap B$ of two algebraic sets A and B , where A , B , and C are numerically represented by witness sets. En route to this result, we first show how to find the irreducible decomposition of a ...
Keywords: components of solutions, polynomial system, embedding, homotopy continuation, generic points, irreducible components, numerical algebraic geometry

20
June 2002 SIAM Journal on Numerical Analysis: Volume 40 Issue 6, 2002
Publisher: Society for Industrial and Applied Mathematics
Bibliometrics:
Citation Count: 17

Many polynomial systems have solution sets comprised of multiple irreducible components, possibly of different dimensions. A fundamental problem of numerical algebraic geometry is to decompose such a solution set, using floating-point numerical processes, into its components. Prior work has shown how to generate sets of generic points guaranteed to include ...
Keywords: Newton identities, Newton interpolation, generic points, irreducible components, numerical algebraic geometry, symmetric functions, components of solutions, divided differences, polynomial system, monodromy, traces, embedding, homotopy continuation



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