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Complexity and Condition in Algebra and Numerics

CORDIS provides links to public deliverables and publications of HORIZON projects.

Links to deliverables and publications from FP7 projects, as well as links to some specific result types such as dataset and software, are dynamically retrieved from OpenAIRE .

Publications

Optimization, complexity and invariant theory

Author(s): Peter Bürgisser
Published in: Proc. 38th International Symposium on Theoretical Aspects of Computer Science, 2021
Publisher: Leibniz-Zentrum für Informatik
DOI: 10.4230/lipics.stacs.2021.1

Gröbner Basis over Semigroup Algebras - Algorithms and Applications for Sparse Polynomial Systems

Author(s): Matías R. Bender, Jean-Charles Faugère, Elias Tsigaridas
Published in: Proceedings of the 2019 on International Symposium on Symbolic and Algebraic Computation, 2019, Page(s) 42-49, ISBN 9781450360845
Publisher: ACM
DOI: 10.1145/3326229.3326248

Polynomial time algorithms in invariant theory for torus actions

Author(s): Peter Bürgisser, Levent Dogan, Visu Makam, Michael Walter
Published in: Proc. 36th Computational Complexity Conference, 2021, 2021
Publisher: Leibniz-Zentrum für Informatik
DOI: 10.4230/lipics.ccc.2021.32

Barriers for recent methods in geodesic optimization

Author(s): Cole Franks, Philipp Reichenbach
Published in: Proc. 36th Computational Complexity Conference, 2021, 2021
Publisher: Leibniz-Zentrum für Informatik
DOI: 10.4230/lipics.ccc.2021.13

Towards a Theory of Non-Commutative Optimization: Geodesic 1st and 2nd Order Methods for Moment Maps and Polytopes

Author(s): Peter Burgisser, Cole Franks, Ankit Garg, Rafael Oliveira, Michael Walter, Avi Wigderson
Published in: 2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS), 2019, Page(s) 845-861, ISBN 978-1-7281-4952-3
Publisher: IEEE
DOI: 10.1109/focs.2019.00055

Random Points on an Algebraic Manifold

Author(s): Paul Breiding, Orlando Marigliano
Published in: SIAM Journal on Mathematics of Data Science, Issue 2/3, 2020, Page(s) 683-704, ISSN 2577-0187
Publisher: SIAM
DOI: 10.1137/19m1271178

Algebraic compressed sensing

Author(s): Paul Breiding; Fulvio Gesmundo; Mateusz Michałe; Nick Vannieuwenhoven
Published in: Applied and Computational Harmonic Analysis, Issue Volume 65, 2023, Page(s) 374-406, ISSN 1063-5203
Publisher: Academic Press
DOI: 10.1016/j.acha.2023.03.006

Certifying Zeros of Polynomial Systems Using Interval Arithmetic

Author(s): Paul Breiding; Kemal Rose; Sascha Timme
Published in: ACM Transactions on Mathematical Software, Issue Volume 49, Issue 121, 2023, Page(s) 1–14, ISSN 0098-3500
Publisher: Association for Computing Machinary, Inc.
DOI: 10.1145/3580277

Cotilting sheaves over weighted noncommutative regular projective curves

Author(s): Dirk Kussin, Rosanna Laking
Published in: Doc. Math. 25, Issue 25, 2020, Page(s) 1029–1077, ISSN 1431-0643
Publisher: DMV
DOI: 10.25537/dm.2020v25.1029-1077

The Average Condition Number of Most Tensor Rank Decomposition Problems is Infinite

Author(s): Carlos Beltran; Paul Breiding; Nick Vannieuwenhoven
Published in: Foundations of Computational Mathematics, Issue 23, pages, 2023, Page(s) 433–491, ISSN 1615-3375
Publisher: Springer Verlag
DOI: 10.1007/s10208-022-09551-1

Sensitivity of low-rank matrix recovery

Author(s): Paul Breiding; Nick Vannieuwenhoven
Published in: Numerische Mathematik, Issue volume 152, 2022, Page(s) 725–759, ISSN 0945-3245
Publisher: Springer Verlag
DOI: 10.1007/s00211-022-01327-7

On the average condition number of tensor rank decompositions

Author(s): Paul Breiding, Nick Vannieuwenhoven
Published in: IMA Journal of Numerical Analysis, Issue 40/3, 2019, Page(s) 1908-1936, ISSN 0272-4979
Publisher: Oxford University Press
DOI: 10.1093/imanum/drz026

The real tau‐conjecture is true on average

Author(s): Irénée Briquel, Peter Bürgisser
Published in: Random Structures & Algorithms, Issue 57/2, 2020, Page(s) 279-303, ISSN 1042-9832
Publisher: John Wiley & Sons Inc.
DOI: 10.1002/rsa.20926

How many eigenvalues of a random symmetric tensor are real?

Author(s): Paul Breiding
Published in: Transactions of the American Mathematical Society, Issue 372/11, 2019, Page(s) 7857-7887, ISSN 0002-9947
Publisher: American Mathematical Society
DOI: 10.1090/tran/7910

Random Spectrahedra

Author(s): Paul Breiding, Khazhgali Kozhasov, Antonio Lerario
Published in: SIAM Journal on Optimization, Issue 29/4, 2019, Page(s) 2608-2624, ISSN 1052-6234
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/18m1208812

Probabilistic Schubert calculus

Author(s): Peter Bürgisser, Antonio Lerario
Published in: Journal für die reine und angewandte Mathematik (Crelles Journal), Issue 2020/760, 2020, Page(s) 1-58, ISSN 0075-4102
Publisher: Walter de Gruyter GmbH & Co. KG
DOI: 10.1515/crelle-2018-0009

On the Number of Real Zeros of Random Fewnomials

Author(s): Peter Bürgisser, Alperen A. Ergür, Josué Tonelli-Cueto
Published in: SIAM Journal on Applied Algebra and Geometry, Issue 3/4, 2019, Page(s) 721-732, ISSN 2470-6566
Publisher: SIAM
DOI: 10.1137/18m1228682

3264 Conics in a Second

Author(s): Sascha Timme, Paul Breiding, Bernd Sturmfels
Published in: Notices of the American Mathematical Society, Issue 67/01, 2020, Page(s) 1, ISSN 0002-9920
Publisher: Mathematical Association of America
DOI: 10.1090/noti2010

An Algebraic Geometric Perspective on Topological Data Analysis

Author(s): Paul Breiding
Published in: SIAM News, Issue 53(1), 2020, ISSN 0003-1224
Publisher: SAGE Publications

Computing the Homology of Semialgebraic Sets. I: Lax Formulas

Author(s): Peter Bürgisser, Felipe Cucker, Josué Tonelli-Cueto
Published in: Foundations of Computational Mathematics, Issue 20/1, 2020, Page(s) 71-118, ISSN 1615-3375
Publisher: Springer Verlag
DOI: 10.1007/s10208-019-09418-y

No occurrence obstructions in geometric complexity theory

Author(s): Peter Bürgisser, Christian Ikenmeyer, Greta Panova
Published in: Journal of the American Mathematical Society, Issue 32/1, 2019, Page(s) 163-193, ISSN 0894-0347
Publisher: American Mathematical Society
DOI: 10.1090/jams/908

Pencil-Based Algorithms for Tensor Rank Decomposition are not Stable

Author(s): Carlos Beltrán, Paul Breiding, Nick Vannieuwenhoven
Published in: SIAM Journal on Matrix Analysis and Applications, Issue 40/2, 2019, Page(s) 739-773, ISSN 0895-4798
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/18m1200531

Computing the Homology of Basic Semialgebraic Sets in Weak Exponential Time

Author(s): Peter Bürgisser, Felipe Cucker, Pierre Lairez
Published in: Journal of the ACM, Issue 66/1, 2019, Page(s) 1-30, ISSN 0004-5411
Publisher: Association for Computing Machinary, Inc.
DOI: 10.1145/3275242

Computing the Homology of Semialgebraic Sets. II: General Formulas

Author(s): Peter Bürgisser, Felipe Cucker, Josué Tonelli-Cueto
Published in: Foundations of Computational Mathematics, 2021, ISSN 1615-3375
Publisher: Springer Verlag
DOI: 10.1007/s10208-020-09483-8

The Condition Number of Riemannian Approximation Problems

Author(s): Paul Breiding, Nick Vannieuwenhoven
Published in: SIAM Journal on Optimization, Issue 31/1, 2021, Page(s) 1049-1077, ISSN 1052-6234
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/20m1323527

Quantitative Singularity Theory for Random Polynomials

Author(s): Paul Breiding, Hanieh Keneshlou, Antonio Lerario
Published in: International Mathematics Research Notices, 2020, ISSN 1073-7928
Publisher: Oxford University Press
DOI: 10.1093/imrn/rnaa274

Euclidean distance degree and mixed volume

Author(s): Paul Breiding; Frank Sottile; James Woodcock
Published in: Foundations of Computational Mathematics, Issue 22, 2022, Page(s) 1743–1765, ISSN 1615-3383
Publisher: Springer Verlag
DOI: 10.1007/s10208-021-09534-8

Invariant Theory and Scaling Algorithms for Maximum Likelihood Estimation

Author(s): Carlos Améndola, Kathlén Kohn, Philipp Reichenbach, Anna Seigal
Published in: SIAM Journal on Applied Algebra and Geometry, Issue 5/2, 2021, Page(s) 304-337, ISSN 2470-6566
Publisher: SIAM
DOI: 10.1137/20m1328932

A nearly optimal algorithm to decompose binary forms

Author(s): Matías R. Bender, Jean-Charles Faugère, Ludovic Perret, Elias Tsigaridas
Published in: Journal of Symbolic Computation, Issue 105, 2021, Page(s) 71-96, ISSN 0747-7171
Publisher: Academic Press
DOI: 10.1016/j.jsc.2020.06.002

Classifier Construction in Boolean Networks Using Algebraic Methods

Author(s): Robert Schwieger, Matías R. Bender, Heike Siebert, Christian Haase
Published in: Computational Methods in Systems Biology - 18th International Conference, CMSB 2020, Konstanz, Germany, September 23–25, 2020, Proceedings, Issue 12314, 2020, Page(s) 210-233, ISBN 978-3-030-60326-7
Publisher: Springer International Publishing
DOI: 10.1007/978-3-030-60327-4_12

Mathematical Software – ICMS 2018 - 6th International Conference, South Bend, IN, USA, July 24-27, 2018, Proceedings

Author(s): Paul Breiding, Sascha Timme
Published in: 2018, ISBN 978-3-319-96418-8
Publisher: Springer
DOI: 10.1007/978-3-319-96418-8

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