janverschelde.github.io/rvchrpub.html at main · janverschelde/janverschelde.github.io · GitHub

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
<HTML>
<HEAD>
<TITLE> Reverse Chronological List of Publications </TITLE>
</HEAD>

<BODY BGCOLOR="#FFFFFF">
<H1> Reverse Chronological List of Publications </H1>
<HR>

<OL>
<LI value=87>
Johnny Joyce and Jan Verschelde:
<B>Computing Linear Regions in Neural Networks with Skip Connections.</B>
In the Proceedings of the 27th International Workshop on Computer Algebra
in Scientific Computing (CASC 2025), edited by F. Boulier, C. Mou,
T.M. Sadykov, and E.V Vorozhtsov, volume 16235 of Lecture Notes
in Computer Science, pages 175-194, Springer-Verlag, 2025.

<P>
<LI value=86>
Johnny Joyce and Jan Verschelde:
<B>Algebraic Representations for Faster Predictions
in Convolutional Neural Networks.</B>
In the Proceedings of the 26th International
Workshop on Computer Algebra in Scientific Computing (CASC 2024),
edited by F. Boulier, C. Mou, T.M. Sadykov, and E.V Vorozhtsov,
volume 14938 of Lecture Notes in Computer Science,
pages 161-177, Springer-Verlag, 2024.

<P>
<LI value=85>
Jan Verschelde:
<B>GPU Accelerated Newton for Taylor Series Solutions
of Polynomial Homotopies in Multiple Double Precision.</B>
In the Proceedings of the 26th International
Workshop on Computer Algebra in Scientific Computing (CASC 2024),
edited by F. Boulier, C. Mou, T.M. Sadykov, and E.V Vorozhtsov,
volume 14938 of Lecture Notes in Computer Science,
pages 328-348, Springer-Verlag, 2024.

<P>
<LI value=84>
Jan Verschelde and Kylash Viswanathan:
<B>Extrapolating Solution Paths of Polynomial Homotopies
towards Singularities with PHCpack and phcpy.</B>
In <EM>Mathematical Software - ICMS 2024</EM>
8th International Conference, Durham, UK, July 22-25.  Proceedings,
edited by K. Buzzard, A. Dickenstein, B. Eick, A. Leykin, and Y. Ren.
Volume 14749 of Lecture Notes in Computer Science,
pages 366-374, Springer, 2024.

<P>
<LI value=83>
Jan Verschelde:
<B>Exporting Ada Software to Python and Julia.</B>
<EM>ACM SIGAda Ada Letters</EM> 42(1):76-78, 2022.

<P>
<LI value=82>
Jan Verschelde and Kylash Viswanathan:
<B>Locating the Closest Singularity in a Polynomial Homotopy.</B>
In the Proceedings of the 24th International
Workshop on Computer Algebra in Scientific Computing (CASC 2022),
edited by F. Boulier, M. England, T.M. Sadykov, and E.V Vorozhtsov,
volume 13366 of Lecture Notes in Computer Science,
pages 333-352, Springer-Verlag, 2022.

<P>
<LI value=81>
Jan Verschelde:
<B>Least Squares on GPUs in Multiple Double Precision.</B>
In the proceedings of the 2022 IEEE International Parallel and
Distributed Processing Symposium Workshops (IPDPSW), pages 828-837,
IEEE, 2022.

<P>
<LI value=80>
Jan Verschelde:
<B>Accelerated Polynomial Evaluation and Differentiation
at Power Series in Multiple Double Precision.</B>
In the proceedings of the 2021 IEEE International Parallel and
Distributed Processing Symposium Workshops (IPDPSW), pages 740-749,
IEEE, 2021.

<P>
<LI value=79>
Anton Leykin, Abraham Martin del Campo,
Frank Sottile, Ravi Vakil, and Jan Verschelde:
<B>Numerical Schubert Calculus via the Littlewood-Richardson
Homotopy Algorithm.</B>
<EM>Mathematics of Computation</EM> 90(329): 1407-1433, 2021.

<P>
<LI value=78>
Jan Verschelde:
<B>Parallel Software to Offset the Cost of Higher Precision.</B>
In the Proceedings of HILT 2020,
<EM>ACM SIGAda Ada Letters</EM> 40(2):59-64, 2020.

<P>
<LI value=77>
Simon Telen, Marc Van Barel, and Jan Verschelde:
<B>A Robust Numerical Path Tracking Algorithm
for Polynomial Homotopy Continuation.</B>
<EM>SIAM Journal on Scientific Computing</EM> 42(6): A3610-A3637, 2020.

<P>
<LI value=76>
Simon Telen, Marc Van Barel, and Jan Verschelde:
<B>Robust Numerical Tracking of One Path of a Polynomial Homotopy
on Parallel Shared Memory Computers.</B>
In the Proceedings of the 22th International
Workshop on Computer Algebra in Scientific Computing (CASC 2020),
edited by F. Boulier, M. England, T.M. Sadykov, W. Seiler, and E.V Vorozhtsov,
volume 12291 of Lecture Notes in Computer Science,
pages 563-582, Springer-Verlag, 2020.

<P><LI value=75>
Jasmine Otto, Angus Forbes, and Jan Verschelde:
<B>Solving Polynomial Systems with phcpy.</B>
In the Proceedings of the 18th Python in Science Conference (SciPy 2019),
edited by Chris Calloway, David Lippa, Dillon Niederhut and David Shupe,
pages 58-64, 2019.

<P><LI value=74>
Jan Verschelde:
<B>A Blackbox Polynomial System Solver on Parallel Shared Memory Computers.</B>
In the Proceedings of the 20th International
Workshop on Computer Algebra in Scientific Computing (CASC 2018),
edited by V.P. Gerdt, W. Koepf, W.M. Seiler, and E.V. Vorozhtsov,
volume 11077 of Lecture Notes in Computer Science,
pages 361-375, Springer-Verlag, 2018.

<P><LI value=73>
Nathan Bliss and Jan Verschelde:
<B>The Method of Gauss-Newton to Compute Power Series Solutions
of Polynomial Homotopies.</B>
<EM>Linear Algebra and Its Applications</EM> 542:569-588, 2018.

<P><LI value=72>
Anders Jensen, Jeff Sommars, and Jan Verschelde:
<B>Computing Tropical Prevarieties in Parallel.</B>
In PASCO 2017: Proceedings of the International Workshop on
Parallel Symbolic Computation, Kaiserslautern, Germany, July 23-24, 2017,
edited by Hans-Wolfgang Loidl, Michael Monagan, Jean-Charles Faugere.

<P> <LI value=71>
Jeff Sommars and Jan Verschelde:
<B>Pruning Algorithms for Pretropisms of Newton Polytopes.</B>
In the Proceedings of the 18th International
Workshop on Computer Algebra in Scientific Computing (CASC 2016),
edited by V.P. Gerdt, W. Koepf, W.M. Seiler, and E.V. Vorozhtsov,
volume 9890 of Lecture Notes in Computer Science,
pages 489-503, Springer-Verlag, 2016.

<P> <LI value=70>
Nathan Bliss and Jan Verschelde:
<B>Computing All Space Curve Solutions of Polynomial Systems
by Polyhedral Methods.</B>
In the Proceedings of the 18th International
Workshop on Computer Algebra in Scientific Computing (CASC 2016),
edited by V.P. Gerdt, W. Koepf, W.M. Seiler, and E.V. Vorozhtsov,
volume 9890 of Lecture Notes in Computer Science,
pages 73-86, Springer-Verlag, 2016.

<P> <LI value=69>
Jeff Sommars and Jan Verschelde:
<B>Computing Pretropisms for the Cyclic n-Roots Problem.</B>
In EuroCG 2016, 32nd European Workshop on Computational Geometry,
EuroCG 2016, Lugano, Switzerland, March 30--April 1, 2016,
pages 235-238.

<P> <LI value=68>
Jan Verschelde and Xiangcheng Yu:
<B>Polynomial Homotopy Continuation on GPUs.</B>
<EM>ACM Communications in Computer Algebra</EM>, volume 49, issue 4,
pages 130-133, 2015.

<P> <LI value=67>
Nathan Bliss, Jeff Sommars, Jan Verschelde, and Xiangcheng Yu:
<B>Solving Polynomial Systems in the Cloud with Polynomial Homotopy
Continuation.</B>
In the Proceedings of the 17th International
Workshop on Computer Algebra in Scientific Computing (CASC 2015),
edited by V.P. Gerdt, W. Koepf, W.M. Seiler, and E.V. Vorozhtsov,
volume 9301 of Lecture Notes in Computer Science,
pages 87-100, Springer-Verlag, 2015.

<P> <LI value=66>
Jan Verschelde and Xiangcheng Yu:
<B>Tracking Many Solution Paths of a Polynomial Homotopy on a
Graphics Processing Unit in Double Double and Quad Double Arithmetic.</B>
In the Proceedings of the 17th IEEE International Conference on High
Performance Computing and Communications (HPCC 2015), pages 371-376,
IEEE Computer Society, 2015.

<P> <LI value=65>
Jan Verschelde and Xiangcheng Yu:
<B>Accelerating Polynomial Homotopy Continuation on a Graphics
Processing Unit with Double Double and Quad Double Arithmetic. </B>
In PASCO 2015, Proceedings of the 7th International
Workshop on Parallel Symbolic Computation,
edited by Jean-Guillaume Dumas and Erich L. Kaltofen,
pages 109-118, ACM 2015.

<P> <LI value=64>
Jan Verschelde and Xiangcheng Yu:
<B>GPU acceleration of Newton's method for large systems of polynomial
equations in double double and quad double arithmetic.</B>
In the Proceedings of the 16th IEEE International Conference on
High Performance Computing and Communication (HPCC 2014),
pages 161-164, IEEE Computer Society, 2014.

<P> <LI value=63>
Jan Verschelde:
<B>modernizing PHCpack through phcpy.</B>
In Proceedings of the 6th European Conference on Python in Science
(EuroSciPy 2013), edited by Pierre de Buyl and Nelle Varoquaux,
pages 71-76, 2014.

<P><LI value=62>
Elizabeth Gross, Sonja Petrovic, and Jan Verschelde:
<B>Interfacing with PHCpack.</B>
<EM>The Journal of Software for Algebra and Geometry</EM> (5):20-25, 2013.

<P><LI value=61>
Danko Adrovic and Jan Verschelde:
<B>Polyhedral Methods for Space Curves Exploiting Symmetry Applied to the
Cyclic n-roots Problem.</B>
In Computer Algebra in Scientific Computing,
15th International Workshop, CASC 2013, Berlin, Germany,
edited by Vladimir P. Gerdt, Wolfram Koepf, Ernst W. Mayr,
and Evgenii V. Vorozhtsov.
Lecture Notes in Computer Science, Volume 8136, pages 10-29,
Springer-Verlag, 2013.

<P><LI value=60>
Jan Verschelde and Genady Yoffe:
<B>Orthogonalization on a General Purpose Graphics Processing Unit
   with Double Double and Quad Double Arithmetic.</B>
In the Proceedings of the 2013 IEEE 27th International Parallel and
Distributed Processing Symposium Workshops (PDSEC 2013).
20-24 May 2013, Boston, Massachusetts.
IEEE Computer Society, 2013, pages 1373-1380.

<P>
<LI value=59>
Danko Adrovic and Jan Verschelde:
<B>Computing Puiseux Series for Algebraic Surfaces.</B>
In the Proceedings of the 37th International Symposium
on Symbolic and Algebraic Computation (ISSAC 2012),
Grenoble, France, July 22-25, 2012.
Edited by Joris van der Hoeven and Mark van Hoeij,
pages 20-27, ACM 2012.

<P>
<LI value=58>
Jan Verschelde and Genady Yoffe:
<B>Evaluating polynomials in several variables and their derivatives
on a GPU computing processor.</B>
In the Proceedings of the 2012 IEEE 26th International
Parallel and Distributed Processing Symposium Workshops (PDSEC 2012).
21-25 May 2012, Shanghai China.  IEEE Computer Society, 2012.
Pages 1391-1399.

<P>
<LI value=57>
Yun Guan and Jan Verschelde:
<B>Sampling Algebraic Sets in Local Intrinsic Coordinates.</B>
<EM>Computers and Mathematics with Applications</EM> 62(10): 3706-2721, 2011.

<P>
<LI value=56>
Danko Adrovic and Jan Verschelde:
<B>Tropical Algebraic Geometry in Maple:
A preprocessing algorithm for finding common factors
to multivariate polynomials with approximate coefficients.</B>
<EM>Journal of Symbolic Computation</EM> 46(7):755-772, 2011.
Special Issue in Honour of Keith Geddes on his 60th Birthday,
edited by Mark W. Giesbrecht and Stephen M. Watt.

<P>
<LI value=55>
Jan Verschelde:
<B>Polynomial Homotopy Continuation with PHCpack.</B>
<EM>ACM Communications in Computer Algebra</EM> 44(4):217-220, 2010.

<P>
<LI value=54>
Frank Sottile, Ravi Vakil, and Jan Verschelde:
<B>Solving Schubert Problems with Littlewood-Richardson Homotopies.</B>
In ISSAC 2010, Proceedings of the
2010 International Symposium on Symbolic and Algebraic Computation,
edited by Stephen M. Watt, pages 179-186, ACM 2010.

<P>
<LI value=53>
Jan Verschelde and Genady Yoffe:
<B>Polynomial Homotopies on Multicore Workstations.</B>
In PASCO 2010, Proceedings of the 2010 International Workshop
on Parallel Symbolic Computation,
edited by Marc Moreno Maza and Jean-Louis Roch,
pages 131-140, ACM 2010.

<P>
<LI value=52>
Kathy Piret and Jan Verschelde:
<B>Sweeping Algebraic Curves for Singular Solutions</B>.
<EM>Journal of Computational and Applied Mathematics</EM> 234(4): 1228-1237, 2010.

<P>
<LI value=51>
Jan Verschelde:
<B>Polyhedral Methods in Numerical Algebraic Geometry</B>.
In <EM>Interactions of Classical and Numerical Algebraic Geometry</EM>,
edited by Dan Bates, GianMario Besana, Sandra Di Rocco,
and Charles Wampler, Contemporary Mathematics 496, pages 243-263, AMS 2009.

<P>
<LI value=50>
Anton Leykin and Jan Verschelde:
<B>Decomposing Solution Sets of Polynomial Systems:
   A New Parallel Monodromy Breakup Algorithm.</B>
<EM>The International Journal of Computational Science and Engineering</EM>
4(2):94-101, 2009.

<P>
<LI value=49>
Yun Guan and Jan Verschelde:
<B>Parallel Implementation of a Subsystem-by-Subsystem Solver</B>.
In the proceedings of the 22th
High Performance Computing Symposium, Quebec City, 9-11 June 2008.
Pages 117-123.  IEEE Computer Society, 2008.

<P>
<LI value=48>
Yun Guan and Jan Verschelde:
<B>PHClab: A MATLAB/Octave interface to PHCpack</B>.
In IMA Volume 148: Software for Algebraic Geometry,
edited by Michael E. Stillman, Nobuki Takayama,
and Jan Verschelde.  Pages 15-32, Springer-Verlag, 2008.

<P> <LI value=47>
Andrew J. Sommese, Jan Verschelde, and Charles W. Wampler:
<B>Solving Polynomial Systems Equation by Equation</B>.
In IMA Volume 146: Algorithms in
Algebraic Geometry, edited by Alicia Dickenstein, Frank-Olaf Schreyer,
and Andrew J. Sommese. Pages 133-152, Springer-Verlag, 2008.

<P> <LI value=46>
Anton Leykin, Jan Verschelde, and Ailing Zhao:
<B>Higher-Order Deflation for Polynomial Systems
with Isolated Singular Solutions.</B>
In IMA Volume 146: Algorithms in
Algebraic Geometry, edited by Alicia Dickenstein, Frank-Olaf Schreyer,
and Andrew J. Sommese. Pages 79-97, Springer-Verlag, 2008.

<P><LI value = 45>
Anton Leykin, Jan Verschelde, and Ailing Zhao:
<B>Evaluation of Jacobian Matrices for Newton's
   Method with Deflation to approximate
   Isolated Singular Solutions of Polynomial Systems.</B>
In <EM>Symbolic-Numeric Computation</EM>,
edited by Dongming Wang and Lihong Zhi.  Pages 269-278.
Trends in Mathematics.  Birkhauser, 2007.

<P> <LI value = 44>
Anton Leykin and Jan Verschelde:
<B>Interfacing with the Numerical Homotopy Algorithms in PHCpack.</B>
In the Proceedings of ICMS 2006,
LNCS 4151, edited by Andrew Iglesias and Nobuki Takayama.
Pages 354-360, Springer-Verlag, 2006.

<P>
<LI value = 43>
Anton Leykin, Jan Verschelde, and Yan Zhuang:
<B>Parallel Homotopy Algorithms to Solve Polynomial Systems.</B>
In the Proceedings of ICMS 2006,
LNCS 4151, edited by Andrew Iglesias and Nobuki Takayama.
Pages 225-234, Springer-Verlag, 2006.

<P>
<LI value = 42> Jan Verschelde and Yan Zhuang:
<B>Parallel Implementation of the Polyhedral Homotopy Method.</B>
Proceedings of the 2006 International Conference on Parallel Processing
Workshops. 14-18 August 2006. Columbus, Ohio.
High Performance Scientific and Engineering Computing.
Edited by Timothy Mark Pinkston and Fusun Ozguner.
Pages 481-488, IEEE Computer Society, 2006.

<P>
<LI value = 41>
Anton Leykin, Jan Verschelde, and Ailing Zhao:
<B>Newton's method with deflation for isolated singularities
   of polynomial systems.</B>
<EM>Theoretical Computer Science</EM> 359(1-3): 111-122, 2006.

<P>

<LI value = 40>
Greg Reid, Jan Verschelde, Allan Wittkopf, and Wenyuan Wu:
<B>Symbolic-Numeric Completion of Differential Systems
   by Homotopy Continuation.</B>
In the Proceedings of the 2005 International Symposium on Symbolic and
Algebraic Computation (ISSAC'05), July 24-27 2005, Beijing, China.
Edited by Manuel Kauers, pages 269-276, ACM 2005.

<P>

<LI value = 39>
Jan Verschelde:
<B>Introduction to Symbolic Computation: a Maple/MATLAB Course</B>.
Maple Conference 2005.  Wilfrid Laurier University.  July 17-21, 2005.
Waterloo Ontario, Canada.  Book of Proceedings.
Edited by Ilias Kotsireas.  Pages 500-509, Maplesoft, 2005.

<P>
<LI value = 38>
Andrew J. Sommese, Jan Verschelde, and Charles W. Wampler:
<B>An intrinsic homotopy for intersecting algebraic varieties</B>.
<EM>Journal of Complexity</EM> 21(4): 593-608, 2005.

<P>
<LI value = 37>
Anton Leykin and Jan Verschelde:
<B>Factoring Solution Sets of Polynomial Systems in Parallel.</B>
In the Proceedings of the 2005 International Conference on Parallel Processing
Workshops.  14-17 June 2005.  Oslo, Norway.
High Performance Scientific and Engineering Computing.
Edited by Tor Skeie and Chu-Sing Yang.
Pages 173-180, IEEE Computer Society, 2005.

<P>
<LI value = 36>
Andrew J. Sommese, Jan Verschelde, and
Charles W. Wampler:
<B>Introduction to Numerical Algebraic Geometry.</B>
In A. Dickenstein and I.Z. Emiris (Eds.),
<EM>Solving Polynomial Equations: Foundations, Algorithms,
and Applications.</EM>  Volume 14 of <EM>Algorithms and Computation in
Mathematics</EM>, Springer-Verlag, pages 339-392, 2005.

<P>
<LI value = 35> Andrew J. Sommese, Jan Verschelde, and
Charles W. Wampler</A>:
<B>Homotopies for intersecting solution components of
   polynomial systems.</B>
<EM>SIAM J. Numerical Anal.</EM> 42(4):1552-1571, 2004.

<P>
<LI value = 34> Jan Verschelde and Yusong Wang:
<B>Computing Dynamic Output Feedback Laws.</B>
<EM>IEEE Transactions on Automatic Control</EM> 49(8):1393-1397, 2004.

<P>

<LI value = 33> Jan Verschelde and Yusong Wang:
  <B>Computing Feedback Laws for Linear Systems
     with a Parallel Pieri Homotopy</B>.
In the Proceedings of the 2004 International Conference on
Parallel Processing Workshops.  15-18 August 2004.
Montreal, Quebec, Canada.
High Performance Scientific and Engineering Computing.
Edited by Yuanyuan Yang.
Pages 222-229, IEEE Computer Society, 2004.

<P>
<LI value = 32>
Anton Leykin and Jan Verschelde:
<B> <EM>PHCmaple</EM>: A Maple Interface to the Numerical Homotopy Algorithms
       in PHCpack. </B>
In the <EM>Proceedings of the Tenth International Conference on
Applications of Computer Algebra</EM> (ACA'2004),
edited by Quoc-Nam Tran, pages 139-147, 2004.

<P>
<LI value = 31>
 Andrew J. Sommese, Jan Verschelde, and Charles W. Wampler:
 <B>Advances in Polynomial Continuation for Solving Problems in Kinematics.</B>
<EM>ASME Journal of Mechanical Design</EM> 126(2):262-268, 2004.
Revised version of what earlier
appeared as Paper DETC2002/MECH-34254,
Proc. ASME Design Engineering Technical Conf. (CDROM),
Montreal, Quebec, Sept. 29-Oct. 2, 2002.

<P>
<LI value = 30>
Andrew J. Sommese, Jan Verschelde, and Charles W. Wampler:
<B>Numerical Factorization of Multivariate Complex Polynomials.</B>
<EM>Theoretical Computer Science</EM> 315(2-3): 651-669, 2004.
Special Issue on Algebraic and Numerical Algorithms
edited by I.Z. Emiris, B. Mourrain, and V.Y. Pan.

<P>
<LI value = 29>
Andrew J. Sommese, Jan Verschelde, and Charles W. Wampler</A>:
<B> Numerical Irreducible Decomposition using PHCpack. </B>
In <EM>Algebra, Geometry and Software Systems</EM>,
edited by M. Joswig and N. Takayama, pages 109-130, Springer-Verlag 2003.

<P>
<LI value = 28>
Andrew J. Sommese, Jan Verschelde, and Charles W. Wampler:
<B> Symmetric Functions Applied to Decomposing
    Solution Sets of Polynomial Systems. </B>
<EM>SIAM J. Numer. Anal.</EM> 40(6):2026-2046, 2002.

<P>
<LI value = 27>
Andrew J. Sommese, Jan Verschelde, and Charles W. Wampler:
<B>A Method for Tracking Singular Paths with Application to
   the Numerical Irreducible Decomposition.</B>
In <EM>Algebraic Geometry, a Volume in Memory of Paolo Francia</EM>
(ed. by M.C. Beltrametti, F. Catanese, C. Ciliberto,
A. Lanteri, C. Pedrini), pages 329-345, W. de Gruyter, 2002.

<P>
<LI value = 26> Jan Verschelde and Yusong Wang:
<B> Numerical Homotopy Algorithms for Satellite Trajectory Control by
    Pole Placement. </B>
In the Proceedings of MTNS 2002, Mathematical Theory of
Networks and Systems (CDROM), Notre Dame, August 12-16, 2002.

<P>
<LI value = 25>
Greg Reid, Chris Smith, and Jan Verschelde:
<B>  Geometric Completion of Differential Systems
     using Numeric-Symbolic Continuation. </B>
<EM>SIGSAM Bulletin </EM> 36(2):1-17, 2002.

<P>
<LI value = 24>
 Andrew J. Sommese, Jan Verschelde, and Charles W. Wampler:
<B> Numerical Irreducible Decomposition using Projections from
    Points on the Components. </B>
In <EM>Symbolic Computation: Solving Equations in Algebra, Geometry, and
Engineering</EM>, edited by E.L. Green, S. Hosten, R. Laubenbacher, and
V.A. Powers. <EM>Contemporary Mathematics</EM>, volume 286, pages 37-51,
AMS 2001.

<P>
<LI value = 23>
Andrew J. Sommese, Jan Verschelde, and Charles W. Wampler:
<B> Using Monodromy to Decompose Solution Sets of Polynomial
    Systems into Irreducible Components. </B>
In <EM>Application of Algebraic Geometry to Coding Theory, Physics,
       and Computation</EM>,
edited by C. Ciliberto, F. Hirzebruch, R. Miranda, and M. Teicher.
Proceedings of a NATO Conference, February 25 - March 1, 2001, Eilat,
Israel.  Pages 297-315, Kluwer Academic Publishers.

<P>
<LI value = 22>
Andrew J. Sommese, Jan Verschelde, and Charles W. Wampler:
<B> Numerical Decomposition of the Solution Sets of Polynomial
    Systems into Irreducible Components. </B>
<EM>SIAM J. Numer. Anal.</EM> 38(6):2022-2046, 2001.

<P>
<LI value = 21>
Andrew J. Sommese and Jan Verschelde:
<B> Numerical Homotopies to compute Generic Points
    on Positive Dimensional Algebraic Sets. </B>
<EM>Journal of Complexity </EM> 16(3):572-602, 2000.

<P>
<LI value = 20> Tangan Gao,
T.Y. Li, Jan Verschelde, and Mengnien Wu:
<B> Balancing the lifting values to improve the
numerical stability of polyhedral homotopy continuation methods. </B>
<EM>Appl. Math. Comput.</EM> 114: 233-247, 2000.

<P>
<LI value = 19> Jan Verschelde:
<B> Numerical Evidence for a Conjecture in Real Algebraic Geometry. </B>
<EM>Experimental Mathematics </EM> 9(2): 183-196, 2000.

<P>
<LI value = 18> Jan Verschelde:
<B> Toric Newton Method for Polynomial Homotopies </B>
<EM>J. Symb. Comput. </EM> 29(4 and 5): 777-793, 2000.

<P>
<LI value = 17> Birkett Huber and Jan Verschelde:
<B> Pieri Homotopies for Problems in Enumerative Geometry
applied to Pole Placement in Linear Systems Control. </B>
<EM>SIAM J. Control Optim. </EM> 38(4): 1265-1287, 2000.

<P>
<LI value = 16> Jan Verschelde:
<B> Algorithm 795: PHCpack: A general-purpose solver for polynomial systems
by homotopy continuation</B>.
<EM>ACM Transactions on Mathematical Software </EM> 25(2): 251-276, 1999.

<P>
<LI value = 15>
Ioannis Z. Emiris and Jan Verschelde:
<B> How to count efficiently all affine roots of a polynomial system</B>.
<EM>Discrete Applied Mathematics</EM> 93(1): 21-32, 1999.

<P>
<LI value = 14> Tom Michiels and Jan Verschelde:
<B> Enumerating Regular Mixed-Cell Configurations</B>.
<EM>Discrete Comput. Geom.</EM> 21(4): 569-579, 1999.

<P>
<LI value = 13> Birkett Huber and Jan Verschelde:
<B> Polyhedral End Games for Polynomial Continuation</B>.
<EM>Numerical Algorithms </EM> 18(1): 91-108, 1998.

<P>
<LI value = 12>Jan Verschelde and Ronald Cools:
<B> Polynomial Homotopy Continuation, A Portable Ada Software Package</B>.
<EM>The Ada-Belgium Newsletter</EM>, 4:59-83, 1996.
In the Proceedings of the 1996 Ada-Belgium Seminar, 22 November 1996,
Eurocontrol, Brussels, Belgium.

<P>
<LI value = 11>Jan Verschelde, Karin Gatermann, and Ronald Cools:
<B> Mixed-Volume Computation by Dynamic Lifting applied to
Polynomial System Solving.</B>
<EM>Discrete Comput. Geom.</EM> 16(1): 69-112, 1996.

<P>
<LI value = 10>Jan Verschelde and Karin Gatermann:
<B> Symmetric Newton Polytopes for Solving Sparse Polynomial Systems.</B>
<EM>Adv. Appl. Math.</EM> 16(1): 95-127, 1995.

<P>
<LI value = 9>Jan Verschelde:
<B> PHC and MVC: two programs for solving polynomial
systems by homotopy continuation</B>.
In the <EM>Proceedings of the POSSO Workshop on Software</EM> pages 165-176.
Edited by J.-C. Faugere, J. Marchand, R. Rioboo, Paris 1-4 March 1995.

<P>
<LI value = 8>Jan Verschelde and Ann Haegemans:
<B> Homotopies for Solving Polynomial Systems within a Bounded Domain.</B>
<EM>Theoretical Comp. Sci. A.</EM> 133(3): 165-185, 1994.

<P>
<LI value = 7>Jan Verschelde, Pierre Verlinden, and Ronald Cools:
<B> Homotopies Exploiting Newton Polytopes for Solving Sparse
Polynomial Systems.</B>
<EM>SIAM J. Numer. Anal.</EM> 31(3):915-930, 1994.

<P>
<LI value = 6>Jan Verschelde and Ronald Cools:
<B> Symmetric Homotopy Construction.</B>
<EM>J. Comput. Appl. Math.</EM> 50:572-592, 1994.

<P>
<LI value = 5>Jan Verschelde and Ronald Cools:
<B> Symbolic Homotopy Construction.</B>
<EM>Applicable Algebra in Engineering, Communication and Computing</EM>
4(3):169-183, 1993.

<P>
<LI value = 4>Jan Verschelde and Ronald Cools:
<B> An Ada Workbench for Homotopy Continuation for Solving
Polynomial Systems.</B>
<EM>The Ada-Belgium Newsletter</EM> 2(1):23-40, 1993.

<P>

<LI value = 3>Jan Verschelde and Ann Haegemans:
<B> The GBQ-Algorithm for Constructing Start Systems of
Homotopies for Polynomial Systems.</B>
<EM>SIAM J. Numer. Anal.</EM> 30(2):583-594, 1993.

<P>
<LI value = 2>Jan Verschelde and Ronald Cools:
<B> Nonlinear Reduction for Solving Deficient Polynomial Systems by
Continuation Methods.</B>
<EM>Numer. Math.</EM> 63(2):263-282, 1992.

<P>
<LI value = 1>Jan Verschelde, Marc Beckers, and Ann Haegemans:
<B> A New Start System for Solving Deficient Polynomial Systems using
Continuation.</B>
<EM>Appl. Math. Comput.</EM> 44(3):225-239, 1991.

</OL>