Emmy Noether research group - Numerical and Probabilistic Nonlinear Algebra

Head:
Paul Breiding (Email)

Phone:
+49 (0) 341 - 9959 - 770

Fax:
+49 (0) 341 - 9959 - 658

Address:
Inselstr. 22
04103 Leipzig

Publications Paul Breiding

Journal Articles

Breiding, Paul ; Sottile, Frank and Woodcock, James: Euclidean distance degree and mixed volume
In: Foundations of computational mathematics, Vol. not yet known, pp. not yet known
Bibtex DOI: 10.1007/s10208-021-09534-8 ARXIV: https://arxiv.org/abs/2012.06350
Journal Open Access

Breiding, Paul and Vannieuwenhoven, Nick: The condition number of Riemannian approximation problems
In: SIAM journal on optimization, 31 (2021) 1, p. 1049-1077
Bibtex DOI: 10.1137/20M1323527 ARXIV: https://arxiv.org/abs/1909.12186
Repository Open Access

Breiding, Paul: An algebraic geometry perspective on topological data analysis
Repository Open Access

Breiding, Paul ; Keneshlou, Hanieh and Lerario, Antonio: Quantitative singularity theory for random polynomials
In: International mathematics research notices, Vol. not yet known, pp. not yet known
Bibtex DOI: 10.1093/imrn/rnaa274 ARXIV: https://arxiv.org/abs/1909.11052
Repository Open Access

Breiding, Paul and Marigliano, Orlando: Random points on an algebraic manifold
In: SIAM journal on mathematics of data science, 2 (2020) 3, p. 683-704
Bibtex MIS-Preprint: 90/2018 DOI: 10.1137/19M1271178 ARXIV: https://arxiv.org/abs/1810.06271
Journal Open Access

Breiding, Paul ; Sturmfels, Bernd and Timme, Sascha: 3264 conics in a second
In: Notices of the American Mathematical Society, 67 (2020) 1, p. 30-37
Bibtex MIS-Preprint: 24/2019 ARXIV: https://arxiv.org/abs/1902.05518 LINK: https://www.ams.org/journals/notices/202001/rnoti-p30.pdf
Journal Open Access

Breiding, Paul and Vannieuwenhoven, Nick: On the average condition number of tensor rank decompositions
In: IMA journal of numerical analysis, 40 (2020) 3, p. 1908-1936
Bibtex MIS-Preprint: 3/2018 DOI: 10.1093/imanum/drz026 ARXIV: https://arxiv.org/abs/1801.01673
Repository Open Access

Beltrán, Carlos ; Breiding, Paul and Vannieuwenhoven, Nick: Pencil-based algorithms for tensor rank decomposition are not stable
In: SIAM journal on matrix analysis and applications, 40 (2019) 2, p. 739-773
Bibtex MIS-Preprint: 48/2018 DOI: 10.1137/18M1200531 ARXIV: https://arxiv.org/abs/1807.04159
Repository Open Access

Breiding, Paul: How many eigenvalues of a random symmetric rensor are real?
In: Transactions of the American Mathematical Society, 372 (2019) 11, p. 7857-7887
Bibtex DOI: 10.1090/tran/7910 ARXIV: https://arxiv.org/abs/1701.07312
Repository Open Access

Breiding, Paul ; Kozhasov, Khazhgali and Lerario, Antonio: Random spectrahedra
In: SIAM journal on optimization, 29 (2019) 4, p. 2608-2624
Bibtex MIS-Preprint: 76/2017 DOI: 10.1137/18M1208812 ARXIV: https://arxiv.org/abs/1711.08253
Repository Open Access

Breiding, Paul ; Kališnik Verovšek, Sara ; Sturmfels, Bernd and Weinstein, Madeleine: Learning algebraic varieties from samples
In: Revista matematica complutense, 31 (2018) 3, p. 545-593
Bibtex MIS-Preprint: 23/2018 DOI: 10.1007/s13163-018-0273-6 ARXIV: https://arxiv.org/abs/1802.09436
Journal Open Access

Breiding, Paul ; Kozhasov, Khazhgali and Lerario, Antonio: On the geometry of the set of symmetric matrices with repeated eigenvalues
In: Arnold mathematical journal, 4 (2018) 3-4, p. 423-443
Bibtex MIS-Preprint: 49/2018 DOI: 10.1007/s40598-018-0095-0 ARXIV: https://arxiv.org/abs/1807.04530
Journal Open Access

Breiding, Paul and Vannieuwenhoven, Nick: Convergence analysis of Riemannian Gauss-Newton methods and its connection with the geometric condition number
In: Applied mathematics letters, 78 (2018), p. 42-50
Bibtex MIS-Preprint: 69/2017 DOI: 10.1016/j.aml.2017.10.009 ARXIV: https://arxiv.org/abs/1708.02488
Repository Open Access

Breiding, Paul and Vannieuwenhoven, Nick: The condition number of join decompositions
In: SIAM journal on matrix analysis and applications, 39 (2018) 1, p. 287-309
Bibtex DOI: 10.1137/17M1142880 ARXIV: https://arxiv.org/abs/1611.08117
Repository Open Access

Breiding, Paul and Vannieuwenhoven, Nick: A Riemannian trust region method for the canonical tensor rank approximation problem
In: SIAM journal on optimization, 28 (2018) 3, p. 2435-2465
Bibtex DOI: 10.1137/17M114618X ARXIV: https://arxiv.org/abs/1709.00033
Repository Open Access

Breiding, Paul: The expected number of eigenvalues of a real Gaussian tensor
In: SIAM journal on applied algebra and geometry, 1 (2017) 1, p. 254-271
Bibtex DOI: 10.1137/16M1089769 ARXIV: https://arxiv.org/abs/1604.03910
Journal Open Access

Breiding, Paul and Bürgisser, Peter: Distribution of the eigenvalues of a random system of homogeneous polynomials
In: Linear algebra and its applications, 497 (2016), p. 88-107
Bibtex DOI: 10.1016/j.laa.2016.02.020 ARXIV: https://arxiv.org/abs/1507.02539
Repository Open Access

Publications in Books and Conference Proceedings

Breiding, Paul and Timme, Sascha: 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. - P. 458-465
(Lecture notes in computer science ; 10931)
Bibtex MIS-Preprint: 1/2018 DOI: 10.1007/978-3-319-96418-8_54 ARXIV: https://arxiv.org/abs/1711.10911
Repository Open Access

Preprints

Breiding, Paul ; Bürgisser, Peter ; Lerario, Antonio and Mathis, Léo: The zonoid algebra, generalized mixed volumes, and random determinants
Repository Open Access

Breiding, Paul ; Celik, Türkü Ozlüm ; Duff, Timothy ; Heaton, Alexander ; Maraj, Aida ; Sattelberger, Anna-Laura ; Venturello, Lorenzo and Yürük, Oğuzhan: Nonlinear algebra and applications
Repository Open Access

Breiding, Paul ; Gesmundo, Fulvio ; Michałek, Mateusz and Vannieuwenhoven, Nick: Algebraic compressed sensing
Repository Open Access

Breiding, Paul ; Ikenmeyer, Christian ; Michałek, Mateusz and Hodges, Reuven: Equations for GL invariant families of polynomials
Repository Open Access

Breiding, Paul ; Rose, Kemal and Timme, Sascha: Certifying zeros of polynomial systems using interval arithmetic
Repository Open Access

Beltrán, Carlos ; Breiding, Paul and Vannieuwenhoven, Nick: The average condition number of most tensor rank decomposition problems is infinite
Repository Open Access

Breiding, Paul and Lerario, Antonio: Lectures on random algebraic geometry [Unpublished work in progress]

Breiding, Paul: An efficient randomized homotopy method to approximate eigenpairs of tensors
Repository Open Access

Academic Theses

Breiding, Paul: Numerical and statistical aspects of tensor decompositions = Numerische und statistische Aspekte von Tensor-Zerlegungen
Dissertation, Technische Universität Berlin, 2017
Bibtex LINK: https://depositonce.tu-berlin.de/handle/11303/6710
Repository Open Access

Breiding, Paul: On a \(p\)-adic newton method
Masterarbeit, Universität Göttingen, 2013
Bibtex LINK: http://page.math.tu-berlin.de/~breiding/ma_breiding.pdf
Repository Open Access

BibTeX Files
Files in Bibtex format

25.10.2021, 05:48