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https://www.nist.gov/itl/math/acmd-seminar-gmres-convergence-and-spectral-properties-approximate-preconditioners-kkt

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# ACMD Seminar: GMRES Convergence and Spectral Properties of Approximate Preconditioners for KKT matrices

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Josef Sifuentes*University of Texas Rio Grande Valley*

Tuesday, August 17, 2021, 3:00 PM EDT (1:00 PM MDT)

**A video of this talk is available to NIST staff in the Math channel on NISTube, which is accessible from the NIST internal home page.**

**Abstract:** Several important preconditioners for saddle point problems yield linear systems for which the GMRES iterative method converges exactly in just a few iterations. However, these preconditioners all involve inverses of large submatrices. In practical computations such inverses are only approximated, and more iterations are required to solve the preconditioned linear system. How many more iterations? In this talk, we present perturbation analysis results for GMRES that leads to rigorous upper bounds on the number of iterations as a function of the accuracy of the preconditioner to the ideal and spectral properties of the constituent matrices. We also derive a thorough analysis of the spectral properties of these common saddle point preconditioners. We will demonstrate some numerical computations that verify these results for problems from optimization and fluid dynamics.

**Bio:**  Josef Sifuentes is an Assistant Professor in the School of Mathematical and Statistical Sciences at the University of Texas Rio Grande Valley. His research focuses on iterative methods in applied mathematics and in particular Krylov subspace methods in numerical linear algebra.

**Note:**This talk will be recorded to provide access to NIST staff and associates who could not be present to the time of the seminar. The recording will be made available in the Math channel on NISTube, which is accessible only on the NIST internal network. This recording could be released to the public through a Freedom of Information Act (FOIA) request. Do not discuss or visually present any sensitive (CUI/PII/BII) material. Ensure that no inappropriate material or any minors are contained within the background of any recording. (To facilitate this, we request that cameras of attendees are muted except when asking questions.)

**Host:**Anthony Kearsley

Mathematics and statistics

## Contacts

                -  Anthony J. Kearsley  anthony.kearsley@nist.gov      (301) 975-6103   
                -  Stephen Langer  stephen.langer@nist.gov      (301) 975-5423   

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