u-generation: solving systems of polynomials equation-by-equation
We develop a new method that improves the efficiency of equation-by-equation homotopy continuation methods for solving polynomial systems. Our method is based on a novel geometric construction and reduces the total number of homotopy paths that must be numerically continued. These improvements may b...
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| Published in | Numerical algorithms Vol. 95; no. 2; pp. 813 - 838 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
New York
Springer US
01.02.2024
|
| Subjects | |
| Online Access | Get full text |
| ISSN | 1017-1398 1572-9265 |
| DOI | 10.1007/s11075-023-01590-1 |
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| Abstract | We develop a new method that improves the efficiency of equation-by-equation homotopy continuation methods for solving polynomial systems. Our method is based on a novel geometric construction and reduces the total number of homotopy paths that must be numerically continued. These improvements may be applied to the basic algorithms of numerical algebraic geometry in the settings of both projective and multiprojective varieties. Our computational experiments demonstrate significant savings obtained on several benchmark systems. We also present an extended case study on maximum likelihood estimation for rank-constrained symmetric
n
×
n
matrices, in which multiprojective
u
-generation allows us to complete the list of ML degrees for
n
≤
6
. |
|---|---|
| AbstractList | We develop a new method that improves the efficiency of equation-by-equation homotopy continuation methods for solving polynomial systems. Our method is based on a novel geometric construction and reduces the total number of homotopy paths that must be numerically continued. These improvements may be applied to the basic algorithms of numerical algebraic geometry in the settings of both projective and multiprojective varieties. Our computational experiments demonstrate significant savings obtained on several benchmark systems. We also present an extended case study on maximum likelihood estimation for rank-constrained symmetric
n
×
n
matrices, in which multiprojective
u
-generation allows us to complete the list of ML degrees for
n
≤
6
. |
| Author | Rodriguez, Jose Israel Duff, Timothy Leykin, Anton |
| Author_xml | – sequence: 1 givenname: Timothy surname: Duff fullname: Duff, Timothy email: timduff@uw.edu organization: Department of Mathematics, University of Washington – sequence: 2 givenname: Anton surname: Leykin fullname: Leykin, Anton organization: School of Mathematics, Georgia Institute of Technology – sequence: 3 givenname: Jose Israel surname: Rodriguez fullname: Rodriguez, Jose Israel organization: Department of Mathematics, University of Wisconsin-Madison |
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| Cites_doi | 10.1090/S0025-5718-1995-1297471-4 10.2140/jsag.2021.11.53 10.1515/advgeom-2020-0006 10.18409/jas.v5i1.23 10.1007/978-0-387-75155-9_8 10.1214/14-AOS1282 10.1137/1.9781611972702 10.1007/978-3-319-96418-8_54 10.1145/3373207.3403995 10.1137/S0036142901397101 10.1007/978-3-662-44199-2_30 10.2140/jsag.2011.3.5 10.1145/120694.120708 10.1145/317275.317286 10.1093/imrn/rnt128 10.1007/978-0-387-75155-9_5 10.1090/gsm/194 10.1090/S0025-5718-2010-02399-3 10.1006/jcom.2000.0554 10.1142/5763 10.1093/imanum/dry017 10.1016/j.jsc.2016.07.019 10.1137/19M1288036 10.1006/jcom.2000.0571 10.1090/mcom/3566 |
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| Copyright_xml | – notice: The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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| Keywords | Regeneration 68W30 Solving polynomials 65H20 14Q65 Numerical algebraic geometry |
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| References | D. J. Bates, J. D. Hauenstein, A. J. Sommese, and C. W. Wampler. Numerically solving polynomial systems with Bertini, volume 25 of Software, Environments, and Tools. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2013 D. R. Grayson and M. E. Stillman. Macaulay2, a software sy,stem for research in algebraic geometry. Available at http://www.math.uiuc.edu/Macaulay2 A. J. Sommese and C. W. Wampler, II. The numerical solution of systems of polynomials. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2005. Arising in engineering and science A. N. Jensen. Tropical homotopy continuation. arXiv preprint arXiv:1601.02818, 2016 S. Katsura. Spin glass problem by the method of integral equation of the effective field. New Trends in Magnetism, pages 110–121, 1990 A. J. Sommese, J. Verschelde, and C. W. Wampler. Solving polynomial systems equation by equation. In Algorithms in algebraic geometry, volume 146 of IMA Vol. Math. Appl., pages 133–152. Springer, New York, 2008 F. Sottile. General witness sets for numerical algebraic geometry. In Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation, ISSAC ’20, page 418–425, New York, NY, USA, 2020. Association for Computing Machinery HuberBSturmfelsBA polyhedral method for solving sparse polynomial systemsMath. Comp.19956421215411555129747110.1090/S0025-5718-1995-1297471-4 S. Sullivant. Algebraic statistics, volume 194 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, 2018 BrysiewiczTRodriguezJISottileFYahlTDecomposable sparse polynomial systemsJ. Softw. Algebra Geom.20211115359428576410.2140/jsag.2021.11.53 VerscheldeJAlgorithm 795: Phcpack: a general-purpose solver for polynomial systems by homotopy continuationACM Transactions on Mathematical Software199925225127610.1145/317275.317286 J. Backelin and R. Fröberg. How we proved that there are exactly 924 cyclic 7-roots. In S. M. Watt, editor, Proceedings of the 1991 International Symposium on Symbolic and Algebraic Computation, ISSAC ’91, Bonn, Germany, July 15-17, 1991, pages 103–111. ACM, 1991 A. J. Sommese and J. Verschelde. Numerical homotopies to compute generic points on positive dimensional algebraic sets. journal of complexity, 16(3):572–602, 2000 HauensteinJDSommeseAJWitness sets of projectionsAppl. Math. Comput.20102177334933542733776 BernsteinDNThe number of roots of a system of equationsFunkcional. Anal. i Priložen.19759314435072 D. Mumford. Stability of projective varieties. Enseign. Math. (2), 23(1-2):39–110, 1977 DuffTHillCJensenALeeKLeykinASommarsJSolving polynomial systems via homotopy continuation and monodromyIMA J. Numer. Anal.201939314211446398406210.1093/imanum/dry017 HauensteinJDWamplerCWUnification and extension of intersection algorithms in numerical algebraic geometryAppl. Math. Comput.20172932262433549665 HauensteinJDSommeseAJWamplerCWRegenerative cascade homotopies for solving polynomial systemsAppl. Math. Comput.20112184124012462831632 D. J. Bates, J. D. Hauenstein, A. J. Sommese, and C. W. Wampler. Bertini: Software for Numerical Algebraic Geometry. Available at bertini.nd.edu with permanent doi: dx.doi.org/10.7274/R0H41PB5 KubjasKRobevaESturmfelsBFixed points EM algorithm and nonnegative rank boundariesAnn. Statist.2015431422461331186510.1214/14-AOS1282 P. Breiding and S. Timme. Homotopycontinuation.jl: A package for homotopy continuation in Julia. In Mathematical Software – ICMS 2018, pages 458–465. Springer International Publishing, 2018 T. Chen, T.-L. Lee, and T.-Y. Li. Hom4ps-3: a parallel numerical solver for systems of polynomial equations based on polyhedral homotopy continuation methods. In International Congress on Mathematical Software, pages 183–190. Springer, 2014 A. J. Sommese, J. Verschelde, and C. W. Wampler. Symmetric functions applied to decomposing solution sets of polynomial systems. SIAM J. Numer. Anal., 40(6):2026–2046 (2003), 2002 GiustiMLecerfGSalvyBA Gröbner free alternative for polynomial system solvingJ. Complexity2001171154211181761210.1006/jcom.2000.0571 HauensteinJDRodriguezJIMultiprojective witness sets and a trace testAdv. Geom.2020203297318412133610.1515/advgeom-2020-0006 HauensteinJDSommeseAJWamplerCWRegeneration homotopies for solving systems of polynomialsMath. Comp.201180273345377272898310.1090/S0025-5718-2010-02399-3 DraismaJRodriguezJMaximum likelihood duality for determinantal varietiesInt. Math. Res. Not. IMRN20142056485666327118410.1093/imrn/rnt128 A. Leykin, J. Verschelde, and A. Zhao. Higher-order deflation for polynomial systems with isolated singular solutions. In Algorithms in algebraic geometry, volume 146 of IMA Vol. Math. Appl., pages 79–97. Springer, New York, 2008 A. N. Jensen. Gfan, a software system for Gröbner fans and tropical varieties. Available at http://home.imf.au.dk/jensen/software/gfan/gfan.html TelenSVan BarelMVerscheldeJA robust numerical path tracking algorithm for polynomial homotopy continuationSIAM J. Sci. Comput.2020426A3610A3637417158910.1137/19M1288036 HauensteinJRodriguezJISturmfelsBMaximum likelihood for matrices with rank constraintsJ. Algebr. Stat.2014511838327995210.18409/jas.v5i1.23 HauensteinJDLeykinARodriguezJISottileFA numerical toolkit for multiprojective varietiesMath. Comp.202190327413440416646710.1090/mcom/3566 A. Martín del Campo and J. I. Rodriguez. Critical points via monodromy and local methods. J. Symbolic Comput., 79(part 3):559–574, 2017 LeykinANumerical algebraic geometryJournal of Software for Algebra and Geometry201131510288126210.2140/jsag.2011.3.5 S Telen (1590_CR34) 2020; 42 1590_CR28 1590_CR27 1590_CR1 M Giusti (1590_CR10) 2001; 17 JD Hauenstein (1590_CR14) 2020; 20 JD Hauenstein (1590_CR16) 2011; 80 1590_CR2 A Leykin (1590_CR24) 2011; 3 1590_CR29 J Draisma (1590_CR8) 2014; 20 1590_CR26 1590_CR25 1590_CR20 1590_CR22 1590_CR21 J Verschelde (1590_CR35) 1999; 25 K Kubjas (1590_CR23) 2015; 43 T Brysiewicz (1590_CR6) 2021; 11 J Hauenstein (1590_CR12) 2014; 5 B Huber (1590_CR19) 1995; 64 T Duff (1590_CR9) 2019; 39 JD Hauenstein (1590_CR15) 2010; 217 1590_CR31 1590_CR30 1590_CR11 1590_CR33 1590_CR32 JD Hauenstein (1590_CR17) 2011; 218 JD Hauenstein (1590_CR18) 2017; 293 JD Hauenstein (1590_CR13) 2021; 90 1590_CR3 1590_CR5 1590_CR7 DN Bernstein (1590_CR4) 1975; 9 |
| References_xml | – reference: HauensteinJDSommeseAJWitness sets of projectionsAppl. Math. Comput.20102177334933542733776 – reference: D. R. Grayson and M. E. Stillman. Macaulay2, a software sy,stem for research in algebraic geometry. Available at http://www.math.uiuc.edu/Macaulay2/ – reference: LeykinANumerical algebraic geometryJournal of Software for Algebra and Geometry201131510288126210.2140/jsag.2011.3.5 – reference: D. J. Bates, J. D. Hauenstein, A. J. Sommese, and C. W. Wampler. Numerically solving polynomial systems with Bertini, volume 25 of Software, Environments, and Tools. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2013 – reference: DuffTHillCJensenALeeKLeykinASommarsJSolving polynomial systems via homotopy continuation and monodromyIMA J. Numer. Anal.201939314211446398406210.1093/imanum/dry017 – reference: J. Backelin and R. Fröberg. How we proved that there are exactly 924 cyclic 7-roots. In S. M. Watt, editor, Proceedings of the 1991 International Symposium on Symbolic and Algebraic Computation, ISSAC ’91, Bonn, Germany, July 15-17, 1991, pages 103–111. ACM, 1991 – reference: A. Leykin, J. Verschelde, and A. Zhao. Higher-order deflation for polynomial systems with isolated singular solutions. In Algorithms in algebraic geometry, volume 146 of IMA Vol. Math. Appl., pages 79–97. Springer, New York, 2008 – reference: D. Mumford. Stability of projective varieties. Enseign. Math. (2), 23(1-2):39–110, 1977 – reference: HuberBSturmfelsBA polyhedral method for solving sparse polynomial systemsMath. Comp.19956421215411555129747110.1090/S0025-5718-1995-1297471-4 – reference: P. Breiding and S. Timme. Homotopycontinuation.jl: A package for homotopy continuation in Julia. In Mathematical Software – ICMS 2018, pages 458–465. Springer International Publishing, 2018 – reference: A. N. Jensen. Gfan, a software system for Gröbner fans and tropical varieties. Available at http://home.imf.au.dk/jensen/software/gfan/gfan.html – reference: BernsteinDNThe number of roots of a system of equationsFunkcional. Anal. i Priložen.19759314435072 – reference: KubjasKRobevaESturmfelsBFixed points EM algorithm and nonnegative rank boundariesAnn. Statist.2015431422461331186510.1214/14-AOS1282 – reference: F. Sottile. General witness sets for numerical algebraic geometry. In Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation, ISSAC ’20, page 418–425, New York, NY, USA, 2020. Association for Computing Machinery – reference: HauensteinJDWamplerCWUnification and extension of intersection algorithms in numerical algebraic geometryAppl. Math. Comput.20172932262433549665 – reference: BrysiewiczTRodriguezJISottileFYahlTDecomposable sparse polynomial systemsJ. Softw. Algebra Geom.20211115359428576410.2140/jsag.2021.11.53 – reference: T. Chen, T.-L. Lee, and T.-Y. Li. Hom4ps-3: a parallel numerical solver for systems of polynomial equations based on polyhedral homotopy continuation methods. In International Congress on Mathematical Software, pages 183–190. Springer, 2014 – reference: HauensteinJDSommeseAJWamplerCWRegenerative cascade homotopies for solving polynomial systemsAppl. Math. Comput.20112184124012462831632 – reference: A. Martín del Campo and J. I. Rodriguez. Critical points via monodromy and local methods. J. Symbolic Comput., 79(part 3):559–574, 2017 – reference: DraismaJRodriguezJMaximum likelihood duality for determinantal varietiesInt. Math. Res. Not. IMRN20142056485666327118410.1093/imrn/rnt128 – reference: A. N. Jensen. Tropical homotopy continuation. arXiv preprint arXiv:1601.02818, 2016 – reference: A. J. Sommese, J. Verschelde, and C. W. Wampler. Symmetric functions applied to decomposing solution sets of polynomial systems. SIAM J. Numer. Anal., 40(6):2026–2046 (2003), 2002 – reference: D. J. Bates, J. D. Hauenstein, A. J. Sommese, and C. W. Wampler. Bertini: Software for Numerical Algebraic Geometry. Available at bertini.nd.edu with permanent doi: dx.doi.org/10.7274/R0H41PB5 – reference: HauensteinJDLeykinARodriguezJISottileFA numerical toolkit for multiprojective varietiesMath. Comp.202190327413440416646710.1090/mcom/3566 – reference: HauensteinJDSommeseAJWamplerCWRegeneration homotopies for solving systems of polynomialsMath. Comp.201180273345377272898310.1090/S0025-5718-2010-02399-3 – reference: A. J. Sommese, J. Verschelde, and C. W. Wampler. Solving polynomial systems equation by equation. In Algorithms in algebraic geometry, volume 146 of IMA Vol. Math. Appl., pages 133–152. Springer, New York, 2008 – reference: GiustiMLecerfGSalvyBA Gröbner free alternative for polynomial system solvingJ. Complexity2001171154211181761210.1006/jcom.2000.0571 – reference: A. J. Sommese and J. Verschelde. Numerical homotopies to compute generic points on positive dimensional algebraic sets. journal of complexity, 16(3):572–602, 2000 – reference: S. Sullivant. Algebraic statistics, volume 194 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, 2018 – reference: S. Katsura. Spin glass problem by the method of integral equation of the effective field. New Trends in Magnetism, pages 110–121, 1990 – reference: HauensteinJRodriguezJISturmfelsBMaximum likelihood for matrices with rank constraintsJ. Algebr. Stat.2014511838327995210.18409/jas.v5i1.23 – reference: HauensteinJDRodriguezJIMultiprojective witness sets and a trace testAdv. Geom.2020203297318412133610.1515/advgeom-2020-0006 – reference: A. J. Sommese and C. W. Wampler, II. The numerical solution of systems of polynomials. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2005. Arising in engineering and science – reference: TelenSVan BarelMVerscheldeJA robust numerical path tracking algorithm for polynomial homotopy continuationSIAM J. Sci. Comput.2020426A3610A3637417158910.1137/19M1288036 – reference: VerscheldeJAlgorithm 795: Phcpack: a general-purpose solver for polynomial systems by homotopy continuationACM Transactions on Mathematical Software199925225127610.1145/317275.317286 – volume: 64 start-page: 1541 issue: 212 year: 1995 ident: 1590_CR19 publication-title: Math. Comp. doi: 10.1090/S0025-5718-1995-1297471-4 – volume: 11 start-page: 53 issue: 1 year: 2021 ident: 1590_CR6 publication-title: J. Softw. Algebra Geom. doi: 10.2140/jsag.2021.11.53 – ident: 1590_CR22 – ident: 1590_CR20 – volume: 20 start-page: 297 issue: 3 year: 2020 ident: 1590_CR14 publication-title: Adv. Geom. doi: 10.1515/advgeom-2020-0006 – volume: 5 start-page: 18 issue: 1 year: 2014 ident: 1590_CR12 publication-title: J. Algebr. Stat. doi: 10.18409/jas.v5i1.23 – ident: 1590_CR30 doi: 10.1007/978-0-387-75155-9_8 – volume: 43 start-page: 422 issue: 1 year: 2015 ident: 1590_CR23 publication-title: Ann. Statist. doi: 10.1214/14-AOS1282 – ident: 1590_CR3 doi: 10.1137/1.9781611972702 – ident: 1590_CR5 doi: 10.1007/978-3-319-96418-8_54 – ident: 1590_CR32 doi: 10.1145/3373207.3403995 – ident: 1590_CR11 – ident: 1590_CR29 doi: 10.1137/S0036142901397101 – ident: 1590_CR7 doi: 10.1007/978-3-662-44199-2_30 – volume: 217 start-page: 3349 issue: 7 year: 2010 ident: 1590_CR15 publication-title: Appl. Math. 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Comp. doi: 10.1090/S0025-5718-2010-02399-3 – ident: 1590_CR28 doi: 10.1006/jcom.2000.0554 – ident: 1590_CR31 doi: 10.1142/5763 – volume: 39 start-page: 1421 issue: 3 year: 2019 ident: 1590_CR9 publication-title: IMA J. Numer. Anal. doi: 10.1093/imanum/dry017 – ident: 1590_CR26 doi: 10.1016/j.jsc.2016.07.019 – volume: 42 start-page: A3610 issue: 6 year: 2020 ident: 1590_CR34 publication-title: SIAM J. Sci. Comput. doi: 10.1137/19M1288036 – ident: 1590_CR2 – volume: 293 start-page: 226 year: 2017 ident: 1590_CR18 publication-title: Appl. Math. Comput. – volume: 17 start-page: 154 issue: 1 year: 2001 ident: 1590_CR10 publication-title: J. Complexity doi: 10.1006/jcom.2000.0571 – volume: 90 start-page: 413 issue: 327 year: 2021 ident: 1590_CR13 publication-title: Math. Comp. doi: 10.1090/mcom/3566 – volume: 218 start-page: 1240 issue: 4 year: 2011 ident: 1590_CR17 publication-title: Appl. Math. Comput. |
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| Title | u-generation: solving systems of polynomials equation-by-equation |
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