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Numerical and Probabilistic Nonlinear Algebra - Publications

Explore the scholarly works of the "Numerical and Probabilistic Nonlinear Algebra" group. Browse journal articles, contributions in books and conference proceedings, academic theses, or discover our research through preprints.

inJournal
2025 Journal Open Access
Paul Breiding, Bernd Sturmfels and Kexin Wang

Computing arrangements of hypersurfaces

In: Journal of software for algebra and geometry, 15 (2025) 1, pp. 11-27
BibTex DOI: 10.2140/jsag.2025.15.11 ArXiv: 2409.09622
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2025 Repository Open Access
Paul Breiding, Mateusz Michałek, Leonid Monin and Simon Telen

The algebraic degree of coupled oscillators

In: Advances in mathematics, 480 (2025) Part B, p. 110492
BibTex DOI: 10.1016/j.aim.2025.110492 ArXiv: 2208.08179
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2025 Repository Open Access
Claire Burrin, Samantha Fairchild and Jon Chaika

Pairs in discrete lattice orbits with applications to Veech surfaces

In: Journal of the European Mathematical Society, (2025)
BibTex DOI: 10.4171/JEMS/1563 ArXiv: 2211.14621 MiS Preprint
inJournal
2024 Journal Open Access
Paul Breiding, Samantha Fairchild, Pierpaola Santarsiero and Elima Shehu

Average degree of the essential variety

In: La matematica, 3 (2024) 2, pp. 753-776
BibTex DOI: 10.1007/s44007-024-00106-0 ArXiv: 2212.01596 MiS Preprint
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2024 Repository Open Access
Paul Breiding, Timothy Duff, Lukas Gustafsson, Felix Rydell and Elima Shehu

Line multiview ideals

In: Communications in algebra, 52 (2024) 10, pp. 4204-4225
BibTex DOI: 10.1080/00927872.2024.2343762 ArXiv: 2303.02066
Book
2024 Journal Open Access
Paul Breiding, Kathlén Kohn and Bernd Sturmfels

Metric algebraic geometry

Cham : Birkhäuser, 2024.
(Oberwolfach Seminars ; 53)
ISBN: 978-3-031-51461-6, ISBN: 978-3-031-51462-3
BibTex DOI: 10.1007/978-3-031-51462-3
inJournal
2024 Repository Open Access
Türkü Özlüm Celik, Samantha Fairchild and Yelena Mandelshtam

Crossing the transcendental divide : from translation surfaces to algebraic curves

In: Experimental mathematics, 33 (2024) 4, pp. 569-587
BibTex DOI: 10.1080/10586458.2023.2203413 ArXiv: 2211.00304 MiS Preprint
inJournal
2024 Journal Open Access
Jon Chaika and Samantha Fairchild

Shrinking rates of horizontal gaps for generic translation surfaces

In: Geometriae dedicata, 218 (2024) 6, p. 104
BibTex DOI: 10.1007/s10711-024-00953-9 ArXiv: 2207.03836 MiS Preprint
inJournal
2023 Repository Open Access
Jayadev S. Athreya, Samantha Fairchild and Howard Masur

Counting pairs of saddle connections

In: Advances in mathematics, 431 (2023), p. 109233
BibTex DOI: 10.1016/j.aim.2023.109233 ArXiv: 2201.08628 MiS Preprint
inJournal
2023 Journal Open Access
Carlos Beltrán, Paul Breiding and Nick Vannieuwenhoven

The average condition number of most tensor rank decomposition problems is infinite

In: Foundations of computational mathematics, 23 (2023) 2, pp. 433-491
BibTex DOI: 10.1007/s10208-022-09551-1 ArXiv: 1903.05527 MiS Preprint
Preprint
2023 Repository Open Access
Viktoriia Borovik and Paul Breiding

A short proof for the parameter continuation theorem

BibTex ArXiv: 2302.14697
inJournal
2023 Repository Open Access
Paul Breiding, Fulvio Gesmundo, Mateusz Michałek and Nick Vannieuwenhoven

Algebraic compressed sensing

In: Applied and computational harmonic analysis, 65 (2023), pp. 374-406
BibTex DOI: 10.1016/j.acha.2023.03.006 ArXiv: 2108.13208
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2023 Repository Open Access
Paul Breiding, Kemal Rose and Sascha Timme

Certifying zeros of polynomial systems using interval arithmetic

In: ACM transactions on mathematical software, 49 (2023) 1, p. 11
BibTex DOI: 10.1145/3580277 ArXiv: 2011.05000
inJournal
2023 Repository Open Access
Paul Breiding, Felix Rydell, Elima Shehu and Angélica Torres

Line multiview varieties

In: SIAM journal on applied algebra and geometry, 7 (2023) 2, pp. 470-504
BibTex DOI: 10.1137/22M1482263 ArXiv: 2203.01694
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2023 Repository Open Access
Paul Breiding, Türkü Özlüm Celik, Timothy Duff, Alexander Heaton, Aida Maraj, Anna-Laura Sattelberger, Lorenzo Venturello and Oğuzhan Yürük

Nonlinear algebra and applications

In: Numerical algebra, control and optimization, 13 (2023) 1, pp. 81-116
BibTex DOI: 10.3934/naco.2021045 ArXiv: 2103.16300
inJournal
2023 Journal Open Access
Paul Breiding, Julia Lindberg, Gabriel Ong and Linus Sommer

Real circles tangent to 3 conics

In: Le Matematiche, 78 (2023) 1, pp. 149-175
BibTex ArXiv: 2211.06876
inJournal
2023 Repository Open Access
Nick Dewaele, Paul Breiding and Nick Vannieuwenhoven

The condition number of many tensor decompositions is invariant under Tucker compression

In: Numerical algorithms, 94 (2023) 2, pp. 1003-1029
BibTex DOI: 10.1007/s11075-023-01526-9 ArXiv: 2106.13034
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2023 Repository Open Access
Nick Dewaele, Paul Breiding and Nick Vannieuwenhoven

Three decompositions of symmetric tensors have similar condition numbers

In: Linear algebra and its applications, 664 (2023), pp. 253-263
BibTex DOI: 10.1016/j.laa.2023.01.020 ArXiv: 2110.04172
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2023 Repository Open Access
Luis David García Puente, Marina Garrote-López and Elima Shehu

Computing algebraic degrees of phylogenetic varieties

In: Algebraic statistics, 14 (2023) 2, pp. 215-231
BibTex DOI: 10.2140/astat.2023.14.215 ArXiv: 2210.02116
Preprint
2022 Repository Open Access
Paul Breiding, Kristian Ranestad and Madeleine Weinstein

Enumerative geometry of curvature of algebraic hypersurfaces

BibTex ArXiv: 2206.09130
inJournal
2022 Journal Open Access
Paul Breiding, Reuven Hodges, Christian Ikenmeyer and Mateusz Michałek

Equations for GL invariant families of polynomials

In: Vietnam journal of mathematics, 50 (2022) 2, pp. 545-556
BibTex DOI: 10.1007/s10013-022-00549-4 ArXiv: 2110.06608
inJournal
2022 Journal Open Access
Paul Breiding, Frank Sottile and James Woodcock

Euclidean distance degree and mixed volume

In: Foundations of computational mathematics, 22 (2022) 6, pp. 1743-1765
BibTex DOI: 10.1007/s10208-021-09534-8 ArXiv: 2012.06350
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2022 Repository Open Access
Paul Breiding, Hanieh Keneshlou and Antonio Lerario

Quantitative singularity theory for random polynomials

In: International mathematics research notices, 2022 (2022) 8, pp. 5685-5719
BibTex DOI: 10.1093/imrn/rnaa274 ArXiv: 1909.11052
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2022 Repository Open Access
Paul Breiding and Nick Vannieuwenhoven

Sensitivity of low-rank matrix recovery

In: Numerische Mathematik, 152 (2022) 4, pp. 725-759
BibTex DOI: 10.1007/s00211-022-01327-7 ArXiv: 2103.00531
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2022 Repository Open Access
Paul Breiding, Peter Bürgisser, Antonio Lerario and Léo Mathis

The zonoid algebra, generalized mixed volumes, and random determinants

In: Advances in mathematics, 402 (2022), p. 108361
BibTex DOI: 10.1016/j.aim.2022.108361 ArXiv: 2109.14996
Preprint
2021 Repository Open Access
Pavle V. M. Blagojević, Paul Breiding and Alexander Heaton

Facet volumes of polytopes

BibTex ArXiv: 2112.08437
inJournal
2021 Repository Open Access
Paul Breiding and Nick Vannieuwenhoven

The condition number of Riemannian approximation problems

In: SIAM journal on optimization, 31 (2021) 1, pp. 1049-1077
BibTex DOI: 10.1137/20M1323527 ArXiv: 1909.12186
inJournal
2021 Repository Open Access
Samantha Fairchild

A higher moment formula for the Siegel-Veech transform over quotients by Hecke triangle groups

In: Groups, geometry, and dynamics, 15 (2021) 1, pp. 57-81
BibTex DOI: 10.4171/GGD/591 ArXiv: 1901.10115
Academic
2021
Samantha Fairchild

Counting social interactions for discrete subsets of the plane

Dissertation, University of Washington, 2021
BibTex Link: www.proquest.com
inJournal
2021 Journal Open Access
Max Goering, Samantha Fairchild and Christian Weiß

Families of well approximable measures

In: Uniform distribution theory, 16 (2021) 1, pp. 53-70
BibTex DOI: 10.2478/udt-2021-0003 ArXiv: 2003.13122
inJournal
2020 Journal Open Access
Paul Breiding, Bernd Sturmfels and Sascha Timme

3264 conics in a second

In: Notices of the American Mathematical Society, 67 (2020) 1, pp. 30-37
BibTex ArXiv: 1902.05518 MiS Preprint
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2020 Journal Open Access
Paul Breiding

An algebraic geometry perspective on topological data analysis

In: SIAM news, 53 (2020) 1, pp. 5-5
BibTex ArXiv: 2001.02098 Link: sinews.siam.org
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2020 Repository Open Access
Paul Breiding and Nick Vannieuwenhoven

On the average condition number of tensor rank decompositions

In: IMA journal of numerical analysis, 40 (2020) 3, pp. 1908-1936
BibTex DOI: 10.1093/imanum/drz026 ArXiv: 1801.01673 MiS Preprint
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2020 Repository Open Access
Paul Breiding and Orlando Marigliano

Random points on an algebraic manifold

In: SIAM journal on mathematics of data science, 2 (2020) 3, pp. 683-704
BibTex DOI: 10.1137/19M1271178 ArXiv: 1810.06271 MiS Preprint
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2019 Repository Open Access
Carlos Beltrán, Paul Breiding and Nick Vannieuwenhoven

Pencil-based algorithms for tensor rank decomposition are not stable

In: SIAM journal on matrix analysis and applications, 40 (2019) 2, pp. 739-773
BibTex DOI: 10.1137/18M1200531 ArXiv: 1807.04159 MiS Preprint
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2019 Repository Open Access
Paul Breiding

How many eigenvalues of a random symmetric rensor are real?

In: Transactions of the American Mathematical Society, 372 (2019) 11, pp. 7857-7887
BibTex DOI: 10.1090/tran/7910 ArXiv: 1701.07312
Preprint
2019
Paul Breiding and Antonio Lerario

Lectures on random algebraic geometry [Unpublished work in progress]

BibTex Link: pbrdng.github.io
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2019 Repository Open Access
Paul Breiding, Khazhgali Kozhasov and Antonio Lerario

Random spectrahedra

In: SIAM journal on optimization, 29 (2019) 4, pp. 2608-2624
BibTex DOI: 10.1137/18M1208812 ArXiv: 1711.08253 MiS Preprint
Preprint
2019 Repository Open Access
Samantha Fairchild, Ilse Haim, Rafael G. Setra, Robert S. Strichartz and Travis Westura

The Abelian sandpile model on fractal graphs

BibTex ArXiv: 1602.03424
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2018 Repository Open Access
Paul Breiding and Nick Vannieuwenhoven

A Riemannian trust region method for the canonical tensor rank approximation problem

In: SIAM journal on optimization, 28 (2018) 3, pp. 2435-2465
BibTex DOI: 10.1137/17M114618X ArXiv: 1709.00033
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2018 Repository Open Access
Paul Breiding and Nick Vannieuwenhoven

Convergence analysis of Riemannian Gauss-Newton methods and its connection with the geometric condition number

In: Applied mathematics letters, 78 (2018), pp. 42-50
BibTex DOI: 10.1016/j.aml.2017.10.009 ArXiv: 1708.02488 MiS Preprint
inBook
2018 Repository Open Access
Paul Breiding and Sascha Timme

HomotopyContinuation.jl : a package for homotopy continuation in Julia

In: Mathematical software ICMS 2018 : 6th international conference, South Bend, IN, USA, July 24-27, 2018, proceedings / James Davenport... (eds.)
Cham : Springer, 2018. - pp. 458-465
(Lecture notes in computer science ; 10931)
BibTex DOI: 10.1007/978-3-319-96418-8_54 ArXiv: 1711.10911 MiS Preprint
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2018 Journal Open Access
Paul Breiding, Sara Kališnik Verovšek, Bernd Sturmfels and Madeleine Weinstein

Learning algebraic varieties from samples

In: Revista matematica complutense, 31 (2018) 3, pp. 545-593
BibTex DOI: 10.1007/s13163-018-0273-6 ArXiv: 1802.09436 MiS Preprint
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2018 Repository Open Access
Paul Breiding, Khazhgali Kozhasov and Antonio Lerario

On the geometry of the set of symmetric matrices with repeated eigenvalues

In: Arnold mathematical journal, 4 (2018) 3-4, pp. 423-443
BibTex DOI: 10.1007/s40598-018-0095-0 ArXiv: 1807.04530 MiS Preprint
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2018 Repository Open Access
Paul Breiding and Nick Vannieuwenhoven

The condition number of join decompositions

In: SIAM journal on matrix analysis and applications, 39 (2018) 1, pp. 287-309
BibTex DOI: 10.1137/17M1142880 ArXiv: 1611.08117
Academic
2017 Repository Open Access
Paul Breiding

Numerical and statistical aspects of tensor decompositions = Numerische und statistische Aspekte von Tensor-Zerlegungen

Dissertation, Technische Universität Berlin, 2017
BibTex DOI: 10.14279/depositonce-6148
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2017 Journal Open Access
Paul Breiding

The expected number of eigenvalues of a real Gaussian tensor

In: SIAM journal on applied algebra and geometry, 1 (2017) 1, pp. 254-271
BibTex DOI: 10.1137/16M1089769 ArXiv: 1604.03910
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2016 Repository Open Access
Paul Breiding and Peter Bürgisser

Distribution of the eigenvalues of a random system of homogeneous polynomials

In: Linear algebra and its applications, 497 (2016), pp. 88-107
BibTex DOI: 10.1016/j.laa.2016.02.020 ArXiv: 1507.02539
Preprint
2015 Repository Open Access
Paul Breiding

An efficient randomized homotopy method to approximate eigenpairs of tensors

BibTex ArXiv: 1512.03284
Academic
2013 Repository Open Access
Paul Breiding

On a \(p\)-adic newton method

Master's thesis, Universität Göttingen, 2013
BibTex Link: page.math.tu-berlin.de
Preprint
2013 Repository Open Access
Aaron Calderon, Samantha Fairchild, Michael Muir, Viorel Nitica and Samuel Simon

Rigid tilings of quadrants by \(L\)-shaped \(n\)-ominoes and notched rectangles

BibTex Link: science.psu.edu