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Mathematics of Computation

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Smoothed analysis for the condition number of structured real polynomial systems


Authors: Alperen A. Ergür, Grigoris Paouris and J. Maurice Rojas
Journal: Math. Comp. 90 (2021), 2161-2184
MSC (2020): Primary 65Y20; Secondary 51F99
DOI: https://doi.org/10.1090/mcom/3647
Published electronically: June 18, 2021
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Abstract: We consider the sensitivity of real zeros of structured polynomial systems to pertubations of their coefficients. In particular, we provide explicit estimates for condition numbers of structured random real polynomial systems and extend these estimates to the smoothed analysis setting.


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Additional Information

Alperen A. Ergür
Affiliation: Technische Universitat Berlin, Institut für Mathematik, Sekretariat MA 3-2, Strasse des 17. Juni 136 10623 Berlin, Germany
Address at time of publication: Mathematics Department, University of Texas at San Antonio, One UTSA Circle, San Antonio, Texas 78249
Email: alperen.ergur@utsa.edu

Grigoris Paouris
Affiliation: Department of Mathematics, Texas A&M University TAMU 3368, College Station, Texas 77843-3368
MR Author ID: 671202
Email: grigoris@math.tamu.edu

J. Maurice Rojas
Affiliation: Department of Mathematics, Texas A&M University TAMU 3368, College Station, Texas 77843-3368
MR Author ID: 354192
ORCID: 0000-0002-1657-2674
Email: rojas@math.tamu.edu

Received by editor(s): December 13, 2018
Received by editor(s) in revised form: July 26, 2019, February 17, 2020, and July 27, 2020
Published electronically: June 18, 2021
Additional Notes: The first author was partially supported by Einstein Foundation, Berlin and by Pravesh Kothari of CMU. The second author was partially supported by Simons Foundation Collaboration grant 527498 and NSF grants DMS-1812240 and CCF-1900881. The third author was partially supported by NSF grants CCF-1409020, DMS-1460766, and CCF-1900881
Article copyright: © Copyright 2021 American Mathematical Society