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1

Numerical Decomposition of the Solution Sets of Polynomial Systems into Irreducible Components

Andrew J. Sommese, Jan Verschelde and Charles W. Wampler

Journal:

SIAM Journal on Numerical Analysis

Year:

2001

Language:

english

File:

PDF, 973 KB

english, 2001

2

Nonlinear reduction for solving deficient polynomial systems by continuation methods

Jan Verschelde, Ronald Cools

Journal:

Numerische Mathematik

Year:

1992

Language:

english

File:

PDF, 928 KB

english, 1992

3

Homotopies Exploiting Newton Polytopes for Solving Sparse Polynomial Systems

Verschelde, Jan, Verlinden, Pierre, Cools, Ronald

Journal:

SIAM Journal on Numerical Analysis

Year:

1994

Language:

english

File:

PDF, 1.79 MB

english, 1994

4

Homotopies Exploiting Newton Polytopes for Solving Sparse Polynomial Systems

Jan Verschelde, Pierre Verlinden and Ronald Cools

Journal:

SIAM Journal on Numerical Analysis

Year:

1994

Language:

english

File:

PDF, 439 KB

english, 1994

5

The GBQ-Algorithm for Constructing Start Systems of Homotopies for Polynomial Systems

Jan Verschelde and Ann Haegemans

Journal:

SIAM Journal on Numerical Analysis

Year:

1993

Language:

english

File:

PDF, 333 KB

english, 1993

6

Algorithm 795: PHCpack: a general-purpose solver for polynomial systems by homotopy continuation

Verschelde, Jan

Journal:

ACM Transactions on Mathematical Software

Year:

1999

Language:

english

File:

PDF, 210 KB

english, 1999

7

[IEEE 2015 IEEE 17th International Conference on High Performance Computing and Communications (HPCC), 2015 IEEE 7th International Symposium on Cyberspace Safety and Security (CSS) and 2015 IEEE 12th International Conf on Embedded Software and Systems (ICESS) - New York, NY, USA (2015.8.24-2015.8.26)] 2015 IEEE 17th International Conference on High Performance Computing and Communications, 2015 IEEE 7th International Symposium on Cyberspace Safety and Security, and 2015 IEEE 12th International Conference on Embedded Software and Systems - Tracking Many Solution Paths of a Polynomial Homotopy on a Graphics Processing Unit in Double Double and Quad Double Arithmetic

Verschelde, Jan, Yu, Xiangcheng

Year:

2015

Language:

english

File:

PDF, 247 KB

english, 2015

8

Numerical Homotopies to Compute Generic Points on Positive Dimensional Algebraic Sets

Andrew J. Sommese, Jan Verschelde

Journal:

Journal of Complexity

Year:

2000

Language:

english

File:

PDF, 218 KB

english, 2000

9

Toric Newton Method for Polynomial Homotopies

Journal:

Journal of Symbolic Computation

Year:

2000

Language:

english

File:

PDF, 346 KB

english, 2000

10

A new start system for solving deficient polynomial systems using continuation

Jan Verschelde, Marc Beckers, Ann Haegemans

Journal:

Applied Mathematics and Computation

Year:

1991

Language:

english

File:

PDF, 720 KB

english, 1991

11

Homotopies for solving polynomial systems within a bounded domain

Jan Verschelde, Ann Haegemans

Journal:

Theoretical Computer Science

Year:

1994

Language:

english

File:

PDF, 1.26 MB

english, 1994

12

Symmetric homotopy construction

Jan Verschelde, Ronald Cools

Journal:

Journal of Computational and Applied Mathematics

Year:

1994

Language:

english

File:

PDF, 1.27 MB

english, 1994

13

Sweeping algebraic curves for singular solutions

Kathy Piret, Jan Verschelde

Journal:

Journal of Computational and Applied Mathematics

Year:

2010

Language:

english

File:

PDF, 375 KB

english, 2010

14

Tropical algebraic geometry in Maple: A preprocessing algorithm for finding common factors for multivariate polynomials with approximate coefficients

Danko Adrovic, Jan Verschelde

Journal:

Journal of Symbolic Computation

Year:

2011

Language:

english

File:

PDF, 579 KB

english, 2011

15

Numerical factorization of multivariate complex polynomials

Andrew J. Sommese, Jan Verschelde, Charles W. Wampler

Journal:

Theoretical Computer Science

Year:

2004

Language:

english

File:

PDF, 293 KB

english, 2004

16

Newton's method with deflation for isolated singularities of polynomial systems

Anton Leykin, Jan Verschelde, Ailing Zhao

Journal:

Theoretical Computer Science

Year:

2006

Language:

english

File:

PDF, 314 KB

english, 2006

17

Preface

Dario Andrea Bini, Victor Y. Pan, Jan Verschelde

Journal:

Theoretical Computer Science

Year:

2008

Language:

english

File:

PDF, 211 KB

english, 2008

18

Symbolic homotopy construction

Jan Verschelde, Ronald Cools

Journal:

Applicable Algebra in Engineering, Communication and Computing

Year:

1993

Language:

english

File:

PDF, 743 KB

english, 1993

19

An intrinsic homotopy for intersecting algebraic varieties

Andrew J. Sommese, Jan Verschelde, Charles W. Wampler

Journal:

Journal of Complexity

Year:

2005

Language:

english

File:

PDF, 251 KB

english, 2005

20

Balancing the lifting values to improve the numerical stability of polyhedral homotopy continuation methods

Tangan Gao, T.Y. Li, Jan Verschelde, Mengnien Wu

Journal:

Applied Mathematics and Computation

Year:

2000

Language:

english

File:

PDF, 140 KB

english, 2000

21

Polyhedral end games for polynomial continuation

Birkett Huber, Jan Verschelde

Journal:

Numerical Algorithms

Year:

1998

Language:

english

File:

PDF, 152 KB

english, 1998

22

Sampling algebraic sets in local intrinsic coordinates

Yun Guan, Jan Verschelde

Journal:

Computers & Mathematics with Applications

Year:

2011

Language:

english

File:

PDF, 387 KB

english, 2011

23

A diagnostic modelling framework to construct indices of biotic integrity: A case study of fish in the Zeeschelde estuary (Belgium)

Paul Quataert, Pieter Verschelde, Jan Breine, Geert Verbeke, Els Goetghebeur, Frans Ollevier

Journal:

Estuarine, Coastal and Shelf Science

Year:

2011

Language:

english

File:

PDF, 503 KB

english, 2011

24

The $GBQ$-Algorithm for Constructing Start Systems of Homotopies for Polynomial Systems

Verschelde, Jan, Haegemans, Ann

Journal:

SIAM Journal on Numerical Analysis

Year:

1993

Language:

english

File:

PDF, 1.36 MB

english, 1993

25

Numerical Decomposition of the Solution Sets of Polynomial Systems into Irreducible Components

Sommese, Andrew J., Verschelde, Jan, Wampler, Charles W.

Journal:

SIAM Journal on Numerical Analysis

Year:

2001

Language:

english

File:

PDF, 286 KB

english, 2001

26

Symmetric Functions Applied to Decomposing Solution Sets of Polynomial Systems

Sommese, Andrew J., Verschelde, Jan, Wampler, Charles W.

Journal:

SIAM Journal on Numerical Analysis

Year:

2002

Language:

english

File:

PDF, 236 KB

english, 2002

27

Homotopies for Intersecting Solution Components of Polynomial Systems

Sommese, Andrew J., Verschelde, Jan, Wampler, Charles W.

Journal:

SIAM Journal on Numerical Analysis

Year:

2004

Language:

english

File:

PDF, 703 KB

english, 2004

28

Pieri Homotopies for Problems in Enumerative Geometry Applied to Pole Placement in Linear Systems Control

Huber, Birkett, Verschelde, Jan

Journal:

SIAM Journal on Control and Optimization

Year:

2000

Language:

english

File:

PDF, 269 KB

english, 2000

29

[ACM Press the 2010 International Symposium - Munich, Germany (2010.07.25-2010.07.28)] Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation - ISSAC '10 - Solving schubert problems with Littlewood-Richardson homotopies

Sottile, Frank, Vakil, Ravi, Verschelde, Jan

Year:

2010

Language:

english

File:

PDF, 791 KB

english, 2010

30

Numerical Evidence for a Conjecture in Real Algebraic Geometry

Verschelde, Jan

Journal:

Experimental Mathematics

Year:

2000

Language:

english

File:

PDF, 9.25 MB

english, 2000

31

[IEEE 2013 IEEE International Symposium on Parallel & Distributed Processing, Workshops and Phd Forum (IPDPSW) - Cambridge, MA, USA (2013.05.20-2013.05.24)] 2013 IEEE International Symposium on Parallel & Distributed Processing, Workshops and Phd Forum - Orthogonalization on a General Purpose Graphics Processing Unit with Double Double and Quad Double Arithmetic

Verschelde, Jan, Yoffe, Genady

Year:

2013

Language:

english

File:

PDF, 313 KB

english, 2013

32

[IEEE 2012 26th IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW) - Shanghai, China (2012.05.21-2012.05.25)] 2012 IEEE 26th International Parallel and Distributed Processing Symposium Workshops & PhD Forum - Evaluating Polynomials in Several Variables and their Derivatives on a GPU Computing Processor

Verschelde, Jan, Yoffe, Genady

Year:

2012

Language:

english

File:

PDF, 378 KB

english, 2012

33

[IEEE 2008 22nd High performance Computing Symposium (HPCS) - Quebec city, QC, Canada (2008.06.9-2008.06.11)] 2008 22nd International Symposium on High Performance Computing Systems and Applications - Parallel Implementation of a Subsystem-by-Subsystem Solver

Guan, Yun, Verschelde, Jan

Year:

2008

Language:

english

File:

PDF, 210 KB

english, 2008

34

[The IMA Volumes in Mathematics and its Applications] Software for Algebraic Geometry Volume 148 || Software for Numerical Algebraic Geometry: A Paradigm and Progress Towards its Implementation

Stillman, Michael, Verschelde, Jan, Takayama, Nobuki

Year:

2008

Language:

english

File:

PDF, 1.12 MB

english, 2008

35

Polynomial homotopy continuation with PHCpack

Verschelde, Jan

Journal:

ACM SIGSAM Bulletin

Year:

2011

Language:

english

File:

PDF, 114 KB

english, 2011

36

Geometric completion of differential systems using numeric-symbolic continuation

Reid, Greg, Smith, Chris, Verschelde, Jan

Journal:

ACM SIGSAM Bulletin

Year:

2002

Language:

english

File:

PDF, 1.26 MB

english, 2002

37

[ACM Press the 2004 international symposium - Santander, Spain (2004.07.04-2004.07.07)] Proceedings of the 2004 international symposium on Symbolic and algebraic computation - ISSAC '04 - Numerical algebraic geometry and symbolic computation

Verschelde, Jan

Year:

2004

Language:

english

File:

PDF, 70 KB

english, 2004

38

[ACM Press the 2005 international symposium - Beijing, China (2005.07.24-2005.07.27)] Proceedings of the 2005 international symposium on Symbolic and algebraic computation - ISSAC '05 - Symbolic-numeric completion of differential systems by homotopy continuation

Reid, Greg, Verschelde, Jan, Wittkopf, Allan, Wu, Wenyuan

Year:

2005

Language:

english

File:

PDF, 215 KB

english, 2005

39

[ACM Press the 4th International Workshop - Grenoble, France (2010.07.21-2010.07.23)] Proceedings of the 4th International Workshop on Parallel and Symbolic Computation - PASCO '10 - Polynomial homotopies on multicore workstations

Verschelde, Jan, Yoffe, Genady

Year:

2010

Language:

english

File:

PDF, 359 KB

english, 2010

40

[ACM Press the 37th International Symposium - Grenoble, France (2012.07.22-2012.07.25)] Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation - ISSAC '12 - Computing Puiseux series for algebraic surfaces

Adrovic, Danko, Verschelde, Jan

Year:

2012

Language:

english

File:

PDF, 378 KB

english, 2012

41

[ACM Press the 2015 International Workshop - Bath, United Kingdom (2015.07.10-2015.07.12)] Proceedings of the 2015 International Workshop on Parallel Symbolic Computation - PASCO '15 - Accelerating polynomial homotopy continuation on a graphics processing unit with double double and quad double arithmetic

Verschelde, Jan, Yu, Xiangcheng

Year:

2015

Language:

english

File:

PDF, 878 KB

english, 2015

42

[IEEE 2014 IEEE International Conference on High Performance Computing and Communications (HPCC), 2014 IEEE 6th International Symposium on Cyberspace Safety and Security (CSS) and 2014 IEEE 11th International Conference on Embedded Software and Systems (ICESS) - Paris, France (2014.8.20-2014.8.22)] 2014 IEEE Intl Conf on High Performance Computing and Communications, 2014 IEEE 6th Intl Symp on Cyberspace Safety and Security, 2014 IEEE 11th Intl Conf on Embedded Software and Syst (HPCC,CSS,ICESS) - GPU Acceleration of Newton's Method for Large Systems of Polynomial Equations in Double Double and Quad Double Arithmetic

Verschelde, Jan, Yu, Xiangcheng

Year:

2014

Language:

english

File:

PDF, 235 KB

english, 2014

43

Symmetric Functions Applied to Decomposing Solution Sets of Polynomial Systems

Andrew J. Sommese, Jan Verschelde and Charles W. Wampler

Journal:

SIAM Journal on Numerical Analysis

Year:

2003

Language:

english

File:

PDF, 611 KB

english, 2003

44

Homotopies for Intersecting Solution Components of Polynomial Systems

Andrew J. Sommese, Jan Verschelde and Charles W. Wampler

Journal:

SIAM Journal on Numerical Analysis

Year:

2005

Language:

english

File:

PDF, 549 KB

english, 2005

45

Polynomial homotopy continuation on GPUs

Verschelde, Jan, Yu, Xiangcheng

Journal:

ACM Communications in Computer Algebra

Year:

2016

Language:

english

File:

PDF, 221 KB

english, 2016

46

Decomposing solution sets of polynomial systems: a new parallel monodromy breakup algorithm

Leykin, Anton, Verschelde, Jan

Journal:

International Journal of Computational Science and Engineering

Year:

2009

Language:

english

File:

PDF, 890 KB

english, 2009

47

TCS SNC Preface

Verschelde, Jan, Watt, Stephen M., Zhi, Lihong

Journal:

Theoretical Computer Science

Year:

2017

Language:

english

File:

PDF, 140 KB

english, 2017

48

The method of Gauss–Newton to compute power series solutions of polynomial homotopies

Bliss, Nathan, Verschelde, Jan

Journal:

Linear Algebra and its Applications

Year:

2017

Language:

english

File:

PDF, 1.72 MB

english, 2017

49

[ASME ASME 2002 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference - Montreal, Quebec, Canada (September 29–October 2, 2002)] Volume 5: 27th Biennial Mechanisms and Robotics Conference - Advances in Polynomial Continuation for Solving Problems in Kinematics

Sommese, Andrew J., Verschelde, Jan, Wampler, Charles W.

Year:

2002

Language:

english

File:

PDF, 138 KB

english, 2002

50

Advances in Polynomial Continuation for Solving Problems in Kinematics

Sommese, Andrew J., Verschelde, Jan, Wampler, Charles W.

Journal:

Journal of Mechanical Design

Year:

2004

Language:

english

File:

PDF, 294 KB

english, 2004